Method and system for providing Low Density Parity Check (LDPC) encoding and decoding

ABSTRACT

An approach is provided for encoding a source signal based on a structured parity check matrix of a Low Density Parity Check (LDPC) code. The LDPC code is represented by stored information reflecting a tabular format of rows and columns, wherein each row represents occurrences of one values within a respective column of the parity check matrix, and wherein the columns of the parity check matrix are derived according to an operation based on the respective rows of the stored information. Blocks of information bits of the source signal are encoded based on the LDPC code to generate an encoded signal. Row indices of 1&#39;s in a column index of the parity check matrix are given at a respective row according to the stored information. The LDPC code is of a structure that facilitates use of a plurality of parallel engines for decoding the encoded signal.

This application is a Continuation-In-Part (CIP) of co-pending U.S.patent application Ser. No. 12/707,766, filed Feb. 18, 2010, titledMethod and System for Providing Low Density Parity Check (LDPC) Encodingand Decoding, which is incorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

Communication systems employ coding to ensure reliable communicationacross noisy communication channels. These communication channelsexhibit a fixed capacity that can be expressed in terms of bits persymbol at certain signal to noise ratio (SNR), defining a theoreticalupper limit (known as the Shannon limit). As a result, coding design hasaimed to achieve rates approaching this Shannon limit. One such class ofcodes that approach the Shannon limit is Low Density Parity Check (LDPC)codes.

Traditionally, LDPC codes have not been widely deployed because of anumber of drawbacks. One drawback is that the LDPC encoding technique ishighly complex. Encoding an LDPC code using its generator matrix wouldrequire storing a very large, non-sparse matrix. Additionally, LDPCcodes require large blocks to be effective; consequently, even thoughparity check matrices of LDPC codes are sparse, storing these matricesis problematic.

From an implementation perspective, a number of challenges areconfronted. For example, storage is an important reason why LDPC codeshave not become widespread in practice. Also, a key challenge in LDPCcode implementation has been how to achieve the connection networkbetween several processing engines (nodes) in the decoder. Further, thecomputational load in the decoding process, specifically the check nodeoperations, poses a problem.

Therefore, there is a need for an LDPC communication system that employssimple encoding and decoding processes. There is also a need for usingLDPC codes efficiently to support high data rates, without introducinggreater complexity. There is also a need to improve performance of LDPCencoders and decoders. There is also a need to minimize storagerequirements for implementing LDPC coding. There is a further need for ascheme that simplifies the communication between processing nodes in theLDPC decoder.

Some Exemplary Embodiments

These and other needs are addressed by the present invention, whereinvarious approaches are provided for encoding and decoding informationbits of a source signal based on structured Low Density Parity Check(LDPC) codes.

According to exemplary embodiments of the present invention, a methodcomprises encoding information bits of a source signal based on astructured parity check matrix of a Low Density Parity Check (LDPC)code. The LDPC code is represented by stored information reflecting atabular format of rows and columns, wherein each row representsoccurrences of one values within a respective column of the parity checkmatrix, and wherein the columns of the parity check matrix are derivedaccording to a predetermined operation based on the respective rows ofthe stored information. One or more blocks of information bits of thesource signal are encoded based on the LDPC code to generate an encodedsignal. The encoding of the blocks of information bits is performedbased on blocks, where each block is of a size of k_(ldpc) informationbits, and the resulting encoded block is of a size of n_(ldpc) code bitsincluding parity bits p_(i), i=0, 1, 2, . . . , n_(ldpc)−k_(ldpc)−1.Parity bit accumulators a_(i) are initialized such that a₀=a₁= . . .=a_(n) _(ldpc) _(−k) _(ldpc−1) =0. For a one of the blocks ofinformation bits, the block is divided into j sequential groups (each ofa size of M information bits), and for j=1, 2, 3, . . . k_(ldpc)/M: (1)a first information bit of a j^(th) group is accumulated in certain ofthe parity bit accumulators reflected by accumulator addresses based ona j^(th) row of the stored information; and (2) the remaining (M−1)information bits of the j^(th) group are accumulated in certain of theparity bit accumulators reflected by accumulator addresses according to{x+m mod M*q} mod(n_(ldpc)−k_(ldpc)), wherein x denotes an address ofthe parity bit accumulator corresponding to the first bit of the group,and q=(n_(ldpc)−k_(ldpc))/M. After all of the information bits of theone block are accumulated, certain operations (e.g., reflecting a singlebelief algorithm) are sequentially performed (with respect to the paritybit accumulators) according to a_(i)=a_(i)⊕a_(i-1), i=1, 2, . . .(n_(ldpc)−k_(ldpc)−1), where the additions are in Galois Field (GF) 2.The parity bits p_(i), i=0, 1, . . . (n_(ldpc)−k_(ldpc)−1) arerespectively reflected by the resulting parity bit accumulators a_(i),i=0, 1, . . . (n_(ldpc)−k_(ldpc)−1). Further, the LDPC code may bestructured to facilitate use of a plurality of parallel engines fordecoding the encoded signal.

According to further exemplary embodiments of the present invention, amethod comprises encoding information bits of a source signal based on astructured parity check matrix of a Low Density Parity Check (LDPC)code. The LDPC code is represented by stored information reflecting atabular format of rows and columns, wherein each row representsoccurrences of one values within a respective column of the parity checkmatrix, and wherein the columns of the parity check matrix are derivedaccording to a predetermined operation based on the respective rows ofthe stored information. One or more blocks of information bits of thesource signal are encoded based on the LDPC code to generate an encodedsignal. The encoding of the blocks of information bits is performedbased on blocks, where each block is of a size of k_(ldpc) informationbits, and the resulting encoded block is of a size of n_(ldpc) code bitsincluding parity bits p_(i), i=0, 1, 2, . . . , n_(ldpc)−k_(ldpc)−1.Parity bit accumulators a_(i) are initialized such that a₀=a₁= . . .=a_(n) _(ldpc) _(−k) _(ldpc) ⁻¹=0. For a one of the blocks ofinformation bits, the block is divided into j sequential groups (each ofa size of M information bits), and for j=1, 2, 3, . . . k_(ldpc)/M: (1)a first information bit of a j^(th) group is accumulated in certain ofthe parity bit accumulators reflected by accumulator addresses based ona j^(th) row of the stored information; and (2) the remaining (M−1)information bits of the j^(th) group are accumulated in certain of theparity bit accumulators reflected by accumulator addresses according to

${\{ {x + {m\mspace{14mu}{mod}\mspace{14mu} M}} \} - {\{ {\frac{x + {m\mspace{14mu}{mod}\mspace{14mu} M}}{M} - \frac{x}{M}} \}*M}},$wherein x denotes an address of the parity bit accumulator correspondingto the first bit of the group. Further, within the brackets { } of thesecond term of the foregoing formula for determining the accumulatoraddresses, the division for each term

$( {{that}\mspace{14mu}{is}{\mspace{11mu}\;}\frac{x + {m\mspace{14mu}{mod}\mspace{14mu} M}}{M}\mspace{14mu}{and}\mspace{14mu}\frac{x}{M}} )$reflects integer division, whereby the result of the division equals theinteger quotient and the numbers to the right of the decimal point areignored). For example, a quotient of 5.952 would be converted to 5 andnot rounded up to 6. As such, the result within the brackets { } shouldbe either 0 or 1. After all of the information bits of the one block areaccumulated, certain operations (e.g., reflecting a layered beliefalgorithm) are sequentially performed (with respect to the parity bitaccumulators). The parity bits p_(i), i=0, 1, . . .(n_(ldpc)−k_(ldpc)−1) are respectively reflected by the resulting paritybit accumulators a_(i), i=0, 1, . . . (n_(ldpc)−k_(ldpc)−1). Further,the LDPC code may be structured to facilitate use of a plurality ofparallel engines for decoding the encoded signal.

Additionally, according to other aspects of exemplary embodiments of thepresent invention, the encoded signal may be modulated according to asignal constellation comprising a one of the following: (1) a QPSK(Quadrature Phase Shift Keying) constellation having bit labeling andx-y bit positioning according to a certain predetermined structure; (2)an 8-PSK (Phase Shift Keying) constellation having bit labeling and x-ybit positioning according to a certain predetermined structure; (3) a16-APSK (Amplitude Phase Shift Keying) constellation, of a 4+12 bit/ringformat, having bit labeling and x-y bit positioning according to acertain predetermined structure; (4) a 32-APSK constellation, of a4+12+16 bit/ring format, having bit labeling and x-y bit positioningaccording to a certain predetermined structure; (5) a 32-APSKconstellation, of a 4+12+16 bit/ring format, having bit labeling and x-ybit positioning according to a certain predetermined structure.

Still other aspects, features, and advantages of the present inventionare readily apparent from the following detailed description, simply byillustrating a number of particular embodiments and implementations,including the best mode contemplated for carrying out the presentinvention. The present invention is also capable of other and differentembodiments, and its several details can be modified in various obviousrespects, all without departing from the spirit and scope of the presentinvention. Accordingly, the drawing and description are to be regardedas illustrative in nature, and not as restrictive.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example, and not by wayof limitation, in the figures of the accompanying drawings and in whichlike reference numerals refer to similar elements and in which:

FIG. 1 illustrates a communications system capable of employingmodulation and coding protocols, in accordance with exemplaryembodiments of the present invention;

FIG. 2A illustrates a block diagram of a transmitter employing an LDPCencoder and a modulator, according to exemplary embodiments of thepresent invention;

FIG. 2B illustrates a block diagram of a BCH encoder, an LDPC encoderand an interleaver, according to exemplary embodiments of the presentinvention;

FIG. 2C illustrates a flow chart of a process for performing shorteningand puncturing in an LDPC coding process, according to exemplaryembodiments of the present invention;

FIG. 2D illustrates a flow chart of a process for performing encoding,interleaving and modulating source information bits, according toexemplary embodiments of the present invention;

FIG. 3A illustrates a block diagram of a receiver, according toexemplary embodiments of the present invention;

FIG. 3B illustrates a flow chart depicting a process for decoding anencoded signal, according to exemplary embodiments of the presentinvention;

FIG. 4 illustrates a sparse parity check matrix, according to anexemplary embodiment of the present invention;

FIG. 5 illustrates a bipartite graph of an LDPC code of the matrix ofFIG. 4, according to an exemplary embodiment of the present invention;

FIG. 6 illustrates a sub-matrix of a sparse parity check matrix,according to an exemplary embodiment of the present invention;

FIGS. 7A-7E illustrate modulation signal constellations, according toexemplary embodiments of the present invention;

FIG. 8 illustrates a block diagram of a chip set that can be utilized inimplementing exemplary embodiments of the present invention; and

FIG. 9 illustrates a block diagram of a computer system that can beutilized in implementing exemplary embodiments of the present invention.

DESCRIPTION OF PREFERRED EMBODIMENTS

A system, method, and software for efficiently encoding and decodingstructured Low Density Parity Check (LDPC) codes are described. In thefollowing description, for the purposes of explanation, numerousspecific details are set forth in order to provide a thoroughunderstanding of the present invention. It is apparent, however, to oneskilled in the art that the present invention may be practiced withoutthese specific details or with an equivalent arrangement. In otherinstances, well-known structures and devices are shown in block diagramform in order to avoid unnecessarily obscuring the present invention.

FIG. 1 illustrates a communications system capable of employingmodulation and coding protocols, in accordance with exemplaryembodiments of the present invention. A digital communications system110 includes a transmitter 112 that generates signal waveforms across acommunication channel 114 to a receiver 116. In this discretecommunications system 110, the transmitter 112 has a message source thatproduces a discrete set of possible messages; each of the possiblemessages has a corresponding signal waveform. These signal waveforms areattenuated, or otherwise altered, by communications channel 114. Tocombat the noise channel 114, LDPC codes are utilized.

The LDPC codes that are generated by the transmitter 112 enable highspeed implementation without incurring any performance loss. Thesestructured LDPC codes output from the transmitter 112 avoid assignmentof a small number of check nodes to the bit nodes already vulnerable tochannel errors by virtue of the modulation scheme (e.g., quadraturephase-shift keying (QPSK), offset quadrature phase-shift keying (OQPSK),8-PSK, 16 amplitude phase-shift keying (16-APSK), 32-APSK, etc.).

Further, such LDPC codes have a parallelizable decoding algorithm(unlike turbo codes), which advantageously involves simple operationssuch as addition, comparison and table look-up. Moreover, carefullydesigned LDPC codes do not exhibit any sign of error floor.

According to one embodiment, the transmitter 112 generates, using arelatively simple encoding technique, LDPC codes based on parity checkmatrices (which facilitate efficient memory access during decoding) tocommunicate with the receiver 116. The transmitter 112 employs LDPCcodes that can outperform concatenated turbo+RS (Reed-Solomon) codes,provided the block length is sufficiently large.

FIG. 2A illustrates a block diagram of a transmitter employing an LDPCencoder and a modulator, according to exemplary embodiments of thepresent invention. As illustrated in FIG. 2A, a transmitter 200 can beequipped with an LDPC encoder 203 that accepts input from an informationsource 201 and outputs coded stream of higher redundancy suitable forerror correction processing at the receiver 116. The information source201 can generate K signals from a discrete alphabet, X. LDPC codes canbe specified with parity check matrices. On the other hand, encodingLDPC codes may require, in general, specifying the generator matrices.Even though it is possible to obtain generator matrices from paritycheck matrices using Gaussian elimination, the resulting matrix is nolonger sparse and storing a large generator matrix can be complex.

Encoder 203 generates signals from alphabet Y to a modulator 205 using asimple encoding technique that makes use of the parity check matrix byimposing structure onto the parity check matrix. According to certainembodiments, a restriction can be placed on the parity check matrix byconstraining certain portion of the matrix to be triangular. Theconstruction of such a parity check matrix is described more fully belowin FIG. 6. FIG. 6 illustrates a sub-matrix of a sparse parity checkmatrix, according to an exemplary embodiment of the present invention.Such a restriction can result in negligible performance loss, andtherefore, constitutes an attractive trade-off.

Modulator 205 maps the encoded messages from encoder 203 to signalwaveforms that are transmitted to a transmit antenna 207, which emitsthese waveforms over the communication channel 114. Accordingly, theencoded messages are modulated and distributed to a transmit antenna207. In certain exemplary embodiments, the modulation can includequadrature phase-shift keying (QPSK), offset quadrature phase-shiftkeying (OQPSK), 8-PSK, 16 amplitude phase-shift keying (16-APSK), and/or32-APSK. According to further exemplary embodiments, further modulationschemes are envisioned. The transmissions from the transmit antenna 207propagate to a receiver, as discussed below.

According to one embodiment, in the context of an OQPSK modulationscheme, for example, four different LDPC code rates are defined, asfollows: 1/2, 2/3, 4/5, and 9/10, where, for each code rate, there are22 different coded block sizes (coded bits), as follows: 720, 960, 1200,1440, 1680, 1920, 2160, 2400, 2640, 2880, 3120, 3360, 3600, 3840, 4080,4320, 4560, 4800, 5040, 5280, 5520 and 5760 coded bits, corresponding tofrom 3 up to 24 slots. Bursts longer than 24 slots may be obtained bycoding multiple shorter LDPC codes of “almost equal” sizes. Of the 22block sizes for each code rate, eight correspond to mother LDPCcodes—which comprise the 720, 960, 1440, 2160, 2880, 3600, 4320, and5760 bit blocks. The other 14 codes can be derived from another blocksize mother code by shortening and puncturing (as described furtherbelow).

According to a further embodiment, in the context of an 8-PSK modulationscheme, for example, three different LDPC code rates are defined, asfollows: 2/3, 4/5, and 8/9, where, for each code rate, there are 15different coded block sizes (coded bits), as follows: 720, 1080, 1440,1800, 2160, 2520, 2880, 3240, 3600, 3960, 4320, 4680, 5040, 5400, and5760, corresponding to from 2 up to 16 slots. Bursts longer than 16slots may be obtained by coding multiple shorter LDPC codes of “almostequal” sizes. Of the 15 block sizes for each code rate, eight correspondto mother LDPC codes—which comprise the 720, 1080, 1440, 2160, 2880,3600, 4320, and 5760 bit blocks. The other 7 codes can be derived fromanother block size mother code by shortening and puncturing (asdescribed further below).

FIG. 2C illustrates a flow chart of a process for performing shorteningand puncturing in an LDPC coding process, according to exemplaryembodiments of the present invention. The number of shortened andpunctured bits are denoted by XS and XP, respectively. With reference toFIG. 2C, for the shortening process, XS bits starting from indexXS_(start) in the input block are set to 0 before encoding (per step221). After encoding, these bits are omitted from the resulting codewordbefore transmission (per steps 223 and 225).

According to one embodiment, at step 227, for example, for puncturingwith rate 9/10 code (e.g., in the context of OQPSK modulation), thefollowing XP systematic bits are not transmitted:i _(k) _(ldpc) _(−17XP+XP) _(offset) ,i _(k) _(ldpc) _(−17(XP−1)+XP)_(offset) ,i _(k) _(ldpc) _(−17(XP−2)+XP) _(offset) , . . . ,i _(k)_(ldpc) _(−17×3+XP) _(offset) ,i _(k) _(ldpc) _(−17×2+XP) _(offset) ,i_(k) _(ldpc) _(−17+XP) _(offset) ;and, as a further example, for puncturing with rate 1/2, 2/3 and 4/5codes, the following XP parity bits are not transmitted:p _(XP) _(offset) ,p _(XP) _(offset) _(+XP) _(period) ,p _(XP) _(offset)_(+2XP) _(period) ,p _(XP) _(offset) _(2XP) _(period) , . . . ,p _(XP)_(offset) _(+(XP−1)XP) _(period) ,where XP_(offset) and XP_(period) are code dependent parameters (notethat the first parity bit is denoted as p₀). For each block size thatdoes not correspond to a mother code size, the parameters related toshortening and puncturing, as well as the mother codes, are given inTable 1κ below (where K and N denote the number of un-coded and codedbits, respectively). Moreover, if K_(Mother) and N_(Mother) denote thenumber of un-coded and coded bits of the mother code, respectively, thenfor the derived code: K=K_(Mother)−XS and N=N_(Mother)−XS−XP.

TABLE 1a Rate/Block Mother Size XS XS_(start) XP XP_(period) X_(offset)Code ½ 1200 120 0 120 6 0 ½ 1440 ½ 1680 240 0 240 4 0 ½ 2160 ½ 1920 1200 120 9 0 ½ 2160 ½ 2400 240 0 240 4 0 ½ 2880 ½ 2640 120 0 120 12 0 ½2880 ½ 3120 240 0 240 7 6 ½ 3600 ½ 3360 120 0 120 15 0 ½ 3600 ½ 3840 2400 240 9 0 ½ 4320 ½ 4080 120 0 120 18 0 ½ 4320 ½ 4560 600 0 600 3 0 ½5760 ½ 4800 480 0 480 3 0 ½ 5760 ½ 5040 360 0 360 8 0 ½ 5760 ½ 5280 2400 240 12 0 ½ 5760 ½ 5520 120 0 120 24 0 ½ 5760 ⅔ 1200 160 480 80 6 0 ⅔1440 ⅔ 1680 320 720 160 3 0 ⅔ 2160 ⅔ 1920 160 720 80 9 0 ⅔ 2160 ⅔ 2400320 960 160 6 0 ⅔ 2880 ⅔ 2640 160 960 80 12 0 ⅔ 2880 ⅔ 3120 320 1200 1607 1 ⅔ 3600 ⅔ 3360 160 1200 80 15 0 ⅔ 3600 ⅔ 3840 320 1440 160 9 0 ⅔ 4320⅔ 4080 160 1440 80 18 0 ⅔ 4320 ⅔ 4560 800 1920 400 3 0 ⅔ 5760 ⅔ 4800 6401920 320 3 0 ⅔ 5760 ⅔ 5040 480 1920 240 8 0 ⅔ 5760 ⅔ 5280 320 1920 160 73 ⅔ 5760 ⅔ 5520 160 1920 80 24 0 ⅔ 5760 ⅘ 1200 192 288 48 6 0 ⅘ 1440 ⅘1680 384 1104 96 4 0 ⅘ 2160 ⅘ 1920 192 432 48 9 0 ⅘ 2160 ⅘ 2400 384 57696 6 0 ⅘ 2880 ⅘ 2640 192 576 48 12 0 ⅘ 2880 ⅘ 3120 384 720 96 7 4 ⅘ 3600⅘ 3360 192 720 48 15 0 ⅘ 3600 ⅘ 3840 384 864 96 9 0 ⅘ 4320 ⅘ 4080 192864 48 18 0 ⅘ 4320 ⅘ 4560 960 1152 240 4 0 ⅘ 5760 ⅘ 4800 768 1152 192 60 ⅘ 5760 ⅘ 5040 576 1152 144 8 0 ⅘ 5760 ⅘ 5280 384 1152 96 12 0 ⅘ 5760 ⅘5520 192 1152 48 24 0 ⅘ 5760 9/10 1200 216 0 24 N/A 9 9/10 1440 9/101680 432 0 48 N/A 3 9/10 2160 9/10 1920 216 0 24 N/A 0 9/10 2160 9/102400 432 0 48 N/A 2 9/10 2880 9/10 2640 216 0 24 N/A 0 9/10 2880 9/103120 432 0 48 N/A 5 9/10 3600 9/10 3360 216 0 24 N/A 1 9/10 3600 9/103840 432 0 48 N/A 2 9/10 4320 9/10 4080 216 0 24 N/A 4 9/10 4320 9/104560 1080 0 120 N/A 0 9/10 5760 9/10 4800 864 0 96 N/A 0 9/10 5760 9/105040 648 0 72 N/A 4 9/10 5760 9/10 5280 432 0 48 N/A 2 9/10 5760 9/105520 216 0 24 N/A 4 9/10 5760

Further, for each mother LDPC code, the degree distribution of bit nodesis given in Table 1b below (where N denotes the total number of bitnodes—the coded block size). For each code, all of the check nodesexcept one have the same degree, namely d_(c)=7 for rate 1/2, d_(c)=11for rate 2/3, d_(c)=20 for rate 4/5, and d_(c)=34 for rate 9/10. Theremaining check node has degree one less.

TABLE 1b Rate 8 7 6 5 4 3 2 1 ½  N/4 N/4 N/2-1 1 ⅔ N/6 N/6  N/3 N/3-1 1⅘ 2N/5 2N/5 N/5-1 1 9/10 N/2 2N/5  N/10-1 1

According to a further embodiment, at step 227, for example, forpuncturing with rate 8/9 code (e.g., in the context of 8-PSKmodulation), the following XP systematic bits are not transmitted:i _(k) _(ldpc) _(−21XP+XP) _(offset) ,i _(k) _(ldpc) _(−21(XP−1)+XP)_(offset) ,i _(k) _(ldpc) _(−21(XP−2)+XP) _(offset) , . . . ,i _(k)_(ldpc) _(−21×3+XP) _(offset) ,i _(k) _(ldpc) _(−21×2+XP) _(offset) ,i_(k) _(ldpc) _(−21+XP) _(offset) ,and, as a further example, for puncturing with rate 2/3 and 4/5 codes,the following XP parity bits are not transmitted:p ₀ ,p _(XP) _(period) ,p _(2XP) _(period) , . . . ,p _((XP−1))_(period) ,where XP_(offset) and XP_(period) are code dependent parameters. Foreach block size that does not correspond to a mother code size, theparameters related to shortening and puncturing, as well as the mothercodes, are given in Table 2a below (where K and N denote the number ofun-coded and coded bits, respectively). Moreover, if K_(Mother) andN_(Mother) denote the number of un-coded and coded bits of the mothercode, respectively, then for the derived code: K=K_(Mother) XS andN=N_(Mother)−XS−XP.

TABLE 2a Rate/Block Mother Size XS XS_(start) XP XP_(period) XP_(offset)Code ⅔ 1800 240 720 120 6 N/A ⅔ 2160 ⅔ 2520 240 960 120 8 N/A ⅔ 2880 ⅔3240 240 1200 120 10 N/A ⅔ 3600 ⅔ 3960 240 1440 120 12 N/A ⅔ 4320 ⅔ 4680720 1920 360 5 N/A ⅔ 5760 ⅔ 5040 480 1920 240 8 N/A ⅔ 5760 ⅔ 5400 2401920 120 16 N/A ⅔ 5760 ⅘ 1800 288 0 72 6 N/A ⅘ 2160 ⅘ 2520 288 0 72 8N/A ⅘ 2880 ⅘ 3240 288 0 72 10 N/A ⅘ 3600 ⅘ 3960 288 0 72 12 N/A ⅘ 4320 ⅘4680 864 0 216 5 N/A ⅘ 5760 ⅘ 5040 576 0 144 8 N/A ⅘ 5760 ⅘ 5400 288 072 16 N/A ⅘ 5760 8/9 1800 320 0 40 N/A 12 8/9 2160 8/9 2520 320 0 40 N/A2 8/9 2880 8/9 3240 320 0 40 N/A 13 8/9 3600 8/9 3960 320 0 40 N/A 3 8/94320 8/9 4680 960 0 120 N/A 4 8/9 5760 8/9 5040 640 0 80 N/A 4 8/9 57608/9 5400 320 0 40 N/A 4 8/9 5760

Further, for each mother LDPC code, the degree distribution of bit nodesis given in Table 2b below (where N denotes the total number of bitnodes—the coded block size). For each code, all of the check nodesexcept one have the same degree, namely d_(c)=11 for rate 2/3, d_(c)=20for rate 4/5, and d_(c)=30 for rate 8/9. The remaining check node hasdegree one less.

TABLE 2b Rate 8 7 6 5 4 3 2 1 ⅔ N/6  N/6  N/3 N/3-1 1 ⅘ 2N/5 2N/5 N/5-11 8/9 4N/9 4N/9 N/9-1 1

With further respect to the LDPC coding, in accordance with exemplaryembodiments, the LDPC encoder systematically encodes an informationblock of size k_(ldpc), i=(0, i₀, i₁, . . . , i_(k) _(ldpc) ⁻¹) into acodeword of size n_(ldpc), c=(i₀, i₁, . . . i_(k) _(ldpc) ⁻¹, p₀, p₁, .. . , p_(n) _(ldpc) _(−k) _(ldpc) ⁻¹). The transmission of the codewordstarts in the given order from i₀ and ends with p_(n) _(ldpc) _(−k)_(ldpc) ⁻¹). The task of the LDPC encoder is to determinen_(ldpc)−k_(ldpc) parity bits (p₀, p₁, . . . , p_(n) _(ldpc) _(−k)_(ldpc) ⁻¹) for every block of k_(ldpc) information bits (i₀, i₁, . . ., i_(k) _(ldpc) ⁻¹). For example, the LDPC encoding process can besummarized as follows:

(1) Initialize the parity bit accumulators a₀=a₁= . . . =a_(n) _(ldpc)_(−k) _(ldpc) ⁻¹=0;

(2) For the first information bit i₀, accumulate i₀ at the respectiveparity bit accumulators according to the accumulator addresses specifiedin the first row of the table for the respective code rate and blocksize (n_(ldpc))—For example, Tables 5a through 5h and Tables 6a through6j (below). In other words, each accumulator address specifies thereference number (i) for the respective accumulator (a_(i)) at which theinformation bit is to be accumulated. For example, for rate 2/3 andblock size 720 (Table 4, below), the following operations are performed:a ₈₃ =a ₈₃ ⊕i ₀a ₁₁₇ =a ₁₁₇ ⊕i ₀a ₁₅₆ =a ₁₅₆ ⊕i ₀a ₁₆₉ =a ₁₆₉ ⊕i ₀a ₂₃₁ =a ₂₃₁ ⊕i ₀a ₁₂₆ =a ₁₂₆ ⊕i ₀a ₁₁₂ =a ₁₁₂ ⊕i ₀a ₁₀₆ =a ₁₀₆ ⊕i ₀

-   -   (where all additions are in Galois Field (GF) 2 or modulo 2).

(3) For the next M−1 information bits i_(m), (m=1, 2, . . . , M−1),accumulate the information bits at the respective parity bitaccumulators according to the accumulator addresses {x+m mod M*q}mod(n_(ldpc)−k_(ldpc)), where x denotes the address of the parity bitaccumulator corresponding to the first bit i₀, M is the number ofcolumns of a respective edge RAM (per Tables 3a and 3b, below), and

$q = {\frac{n_{ldpc} - k_{ldpc}}{M}.}$Continuing with the rate 2/3 and block size 720 example (Table 4), withM=30 and q=8, for information bit i₁, the following operations areperformed:a ₉₁ =a ₉₁ ⊕i ₁a ₁₂₅ =a ₁₂₅ ⊕i ₁a ₁₆₄ =a ₁₆₄ ⊕i ₁a ₁₇₇ =a ₁₇₇ ⊕i ₁a ₂₃₉ =a ₂₃₉ ⊕i ₁a ₁₃₄ =a ₁₃₄ ⊕i ₁a ₁₂₀ =a ₁₂₀ ⊕i ₁a ₁₁₄ =a ₁₁₄ ⊕i ₁

-   -   (where all additions are in GF (2)).

(4) For the (M+1)^(st) information bit i_(M), accumulate i_(M) at therespective parity bit accumulators according to the accumulatoraddresses specified in the second row of the respective parity bitaccumulator address table. Then, in a similar manner as in (3), for thenext M−1 information bits i_(m), (m=M+1, M+2, . . . , 2M−1), accumulatethe information bits at the respective parity bit accumulators accordingto the addresses {x+m mod M*q} mod(n_(ldpc)−k_(ldpc)), where x denotesthe address of the parity bit accumulator corresponding to theinformation bit i_(M) (e.g., based on the entries in the second row ofthe respective parity bit accumulator address table).

(5) In a similar manner, for every group of M new information bits,accumulate the information bits at the respective parity accumulatorsbased on accumulator addresses obtained from a new row of the respectiveparity bit accumulator address table and the formula {x+m mod M*q}mod(n_(ldpc)−k_(ldpc)).

(6) After all of the information bits are exhausted, the final paritybits of the codeword are obtained as follows: (a) starting with i=1,sequentially perform the following operations (e.g., single beliefoperations or a single belief algorithm for a single belief decodingmode) with respect to the parity bit accumulators a_(i),a_(i)=a_(i)⊕a_(i-1), for i=1, 2, . . . , n_(ldpc)−k_(ldpc)−1; and (b)the final content of the parity bits p_(i) of the codeword c=(i₀, i₁, .. . i_(k) _(ldpc) ⁻¹, p₀, p₁, . . . p_(n) _(ldpc) _(−k) _(ldpc) ⁻¹) arereflected by the resulting parity bit accumulators a_(i), (i=0, 1, . . ., n_(ldpc)−k_(ldpc)−1).

TABLE 3a Code Rate - Block Size M ½ - 720 60 ½ - 960 60 ½ - 1440 60 ½ -2160 60 ½ - 2880 60 ½ - 3600 60 ½ - 4320 60 ½ - 5760 60 ⅔ - 720 30 ⅔ -960 40 ⅔ - 1440 60 ⅔ - 2160 60 ⅔ - 2880 60 ⅔ - 3600 60 ⅔ - 4320 60 ⅔ -5760 64 ⅘ - 720 48 ⅘ - 960 32 ⅘ - 1440 48 ⅘ - 2160 54 ⅘ - 2880 64 ⅘ -3600 60 ⅘ - 4320 54 ⅘ - 5760 64 9/10 - 720 36 9/10 - 960 48 9/10 - 144036 9/10 - 2160 54 9/10 - 2880 48 9/10 - 3600 60 9/10 - 4320 54 9/10 -5760 64

TABLE 3b Code Rate - Block Size M ⅔ - 720 30 ⅔ - 1080 45 ⅔ - 1440 60 ⅔ -2160 60 ⅔ - 2880 60 ⅔ - 3600 60 ⅔ - 4320 60 ⅔ - 5760 64 ⅘ - 720 48 ⅘ -1080 36 ⅘ - 1440 48 ⅘ - 2160 54 ⅘ - 2880 64 ⅘ - 3600 60 ⅘ - 4320 54 ⅘ -5760 64 8/9 - 720 40 8/9 - 1080 30 8/9 - 1440 40 8/9 - 2160 60 8/9 -2880 64 8/9 - 3600 50 8/9 - 4320 60 8/9 - 5760 64

TABLE 4 Address of Parity Bit Accumulators (Rate ⅔ - Coded Block Size720) 83 117 156 169 231 126 112 106 120 169 106 27 188 213 22 159 160121 106 203 196 141 174 135 64 137 226 91 180 85 166 7 82 7 198 148 13424 9 83 149 160 1 151 74 203 116 13 206 12 101 200 45 98 16 235 165 16725 171 2 83 33 8 174 207 36 170 207 73 172 86

TABLE 5a Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 720) 10 62 53 15 54 56 5 3 8 34 23 45 10 60 23 27 6 70 51 65 26 3823 67 18 22 25 1 12 28 5 61 36 44 7 49 20 46 29 69 6 22 31 46 37 51 5418 65 32 11 17 46 32 15 0 3 45 44 24 63 64 45 23

TABLE 5b Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 960) 88 70 81 43 6 64 29 13 18 82 1 35 10 6 47 53 38 22 57 1 78 687 15 78 48 73 37 26 82 13 17 52 62 19 29 58 14 79 27 86 16 19 2 7 95 4430 5 42 81 13 22 66 17 8 93 19 82 50 41 16 93 57

TABLE 5c Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 1440) 132 109 122 67 12 97 46 19 120 129 70 31 28 125 2 55 108 81134 59 136 49 30 139 40 69 38 123 100 141 46 75 64 109 134 47 120 29 2667 112 37 10 55 136 53 122 103 80 17 34 115 40 61 46 71 132 81 18 7 12113 6 143 108 113 122 11 108 69 110 63 124 141 2 115 100 133 18 15 133 051 106 40 115 101 62 67 136 17 50 80 10 75 37 126 19 40 25 122 40 129143 12 66 83 17 7 74 52 17 23 8 21 94 117 119 80 70 104 25 66 43 73 8898 111

TABLE 5d Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 2160) 36 153 142 127 136 157 182 151 108 197 106 63 108 49 182 35 889 134 43 56 105 30 175 104 181 66 115 96 5 78 211 52 57 194 119 128 972 23 196 37 2 171 184 177 10 15 56 17 2 43 84 121 142 35 8 21 62 107 184193 46 7 160 205 42 107 120 181 122 103 196 153 46 163 72 105 202 11 3186 157 176 186 129 0 27 201 140 154 191 155 6 105 124 118 55 44 197 8760 189 206 121 8 215 206 93 43 136 94 65 28 178 51 110 59 144 149 98 12149 107 184 61 122 99

TABLE 5e Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 2880) 92 133 95 39 78 91 251 284 262 92 89 204 15 226 74 150 73 3928 47 258 175 57 160 171 286 97 12 208 69 108 59 164 4 171 217 50 245171 139 18 122 35 97 30 26 160 53 81 72 286 20 236 259 66 105 11 0 146 7196 95 168 194 1 129 64 29 241 177 250 47 151 53 184 192 59 52 21 84 24887 264 280 103 278 137 154 175 56 273 192 43 80 183 95 134 245 142 33229 18 196 200 186 188 251 33 43 33 250 74 6 55 77 261 282 139 286 227135 163 89 252 151 250 138 286 205 32 137 4 44 87 137 192 158 189 138 50173 236 15 94 82 285 281 133 249 191 114 1 128 96 193 76 1 242 153 284156 53 42 92 160 113 247 81 196 275 103 168 117 262 116 166 137 177 8125 115 9 6 199 219 18 208 138 73 14 154 101

TABLE 5f Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 3600) 212 271 274 5 122 345 127 59 138 71 189 157 60 256 26 143 234105 190 224 240 217 129 58 135 2 349 221 227 336 171 194 358 169 77 33034 235 174 269 74 261 28 235 126 50 345 130 302 42 31 15 214 47 79 33989 180 178 9 38 192 89 49 332 256 222 183 187 140 88 137 213 307 190 137225 258 289 233 188 336 85 93 98 352 333 17 324 62 244 149 108 19 242292 340 303 65 150 166 95 282 169 278 61 113 234 122 207 52 107 37 296135 178 330 271 200 339 176 243 203 284 202 249 210 350 9 61 126 16 253317 108 91 298 287 160 237 31 72 247 124 38 347 169 113 346 24 266 21108 188 267 269 298 117 275 332 216 163 317 130 146 272 82 193 30 129 77282 7 327 292 319 5 99 276 305 125 169 303 80 225 60 92 304 7 36 86 46

TABLE 5g Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 4320) 273 190 207 371 331 258 135 416 306 12 291 293 262 215 396 7414 193 91 207 384 341 260 81 128 365 170 9 336 396 413 238 16 407 130 442 323 54 85 6 103 349 176 216 286 426 277 425 416 419 322 289 164 379189 1 292 319 363 345 132 134 423 366 146 381 235 88 111 206 4 121 426307 254 203 244 406 216 7 275 53 76 329 418 416 84 233 293 351 368 153410 101 183 196 400 170 65 192 357 31 43 46 245 428 304 51 1 144 351 319321 413 298 350 213 244 210 387 166 367 228 297 178 83 238 97 428 266165 197 423 115 265 43 104 172 122 144 227 407 65 166 210 73 311 94 351154 357 64 172 30 13 320 243 412 318 392 346 252 286 13 207 208 277 17867 161 394 351 45 17 295 196 251 326 356 145 168 411 262 54 51 177 398148 355 330 168 399 161 312 50 419 65 327 61 374 232 28 69 303 298 116221 52 270 165 103 398 283 243 184 364 348 7 209 362 221 187 343 184 190265 306 277 56 25 34 325 345 60 198 344 113 68 41 171 253 56 188 431 27256 106 421 22 274 279 67 298 294 79

TABLE 5h Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 5760) 35 247 105 399 280 268 513 68 161 104 460 466 156 253 305 39372 489 178 202 398 199 151 383 92 527 54 224 200 409 42 147 459 569 553312 242 180 155 10 216 458 361 318 104 489 206 52 22 56 123 538 264 295130 29 263 28 274 239 276 124 449 21 360 482 519 253 225 202 212 312 268338 558 200 43 291 436 27 84 231 40 521 95 142 558 361 475 462 319 41984 74 522 573 451 188 526 263 226 159 440 491 415 434 60 215 553 250 72209 18 436 311 210 327 524 536 18 15 211 11 453 22 452 289 305 351 187343 240 98 33 493 147 100 176 188 384 379 347 349 332 532 518 483 445496 203 269 304 459 344 311 574 128 429 538 527 479 125 43 508 228 315416 231 417 558 501 190 498 526 341 505 270 381 517 260 12 481 91 44 540104 339 295 172 467 569 121 137 474 221 567 444 506 104 526 327 547 134519 522 262 547 37 375 377 455 400 327 325 213 390 6 167 11 363 160 541337 185 61 225 7 233 450 407 323 288 38 463 95 274 279 377 423 411 227558 156 114 497 471 22 73 296 508 393 182 304 239 183 415 322 332 28 500106 470 358 505 461 302 342 68 255 90 416 368 487 177 531 161 84 314 391310 392 367 177 19 102 130 366 25

TABLE 6a Address of Parity Bit Accumulators (Rate ⅔ - Coded Block Size1080) 78 323 226 335 169 288 12 213 328 321 122 163 12 37 310 223 344 97346 195 180 325 22 311 56 121 26 187 148 109 302 119 332 251 289 166 19724 303 313 258 228 239 181 232 154 323 182 6 282 77 162 3 199 295 112251 33 50 61 139 208 95 228 121 216 356 302 349 201 324 14

TABLE 6b Address of Parity Bit Accumulators (Rate ⅘ - Coded Block Size1080) 90 67 188 117 28 125 186 1 146 99 22 197 60 85 44 147 118 41 42133 8 75 142 17 30 97 158 93 46 71 30 109 182 195 16 143 60 10 105 33166 185 142 85 168 86 133 159 104 137 91 24 110 167 31 36 46 142 186 6389 139 116 99 5 88 176 195 193 12 44 185 168 37 146 141 166 101 66 37200 45 136 89 90 19 152 111 94 179 84 211 26 183 64 113 60 1 80 129 190179 6 121 20 159 88 131

TABLE 6c Address of Parity Bit Accumulators (Rate 8/9 - Coded Block Size720) 34 78 37 17 72 76 43 35 2 4 79 37 40 60 51 17 4 70 59 49 50 22 6331 46 20 69 73 40 70 57 55 38 22 43 46 40 71 14 17 61 26 21 45 4 36 1 6026 33 46 55 21 36 27 13

TABLE 6d Address of Parity Bit Accumulators (Rate 8/9 - Coded Block Size1080) 20 77 70 31 96 45 86 3 24 65 34 3 0 21 74 67 28 5 106 71 16 41 1895 72 17 6 59 40 69 22 71 64 101 86 83 96 85 46 119 96 37 70 99 0 89 4659 80 65 74 63 44 57 102 79 76 5 54 115 8 109 74 119 32 105 118 48 57 6244 89 30 80 97 114 60 65 115 40 5 111 52 9 27 108 105 79 116 38 47 32 3879 36 34 51 56 94 119 49 114 119 21 78 51 1 22 87 37 66 15

TABLE 6e Address of Parity Bit Accumulators (Rate 8/9 - Coded Block Size1440) 68 49 138 87 16 89 62 39 140 1 106 75 12 141 46 67 100 9 26 87 1241 94 83 128 73 106 35 20 113 10 55 16 81 122 135 136 97 38 111 140 77102 143 60 105 86 71 88 61 130 39 136 121 134 75 92 145 98 151 12 5 50 764 125 94 152 9 6 56 9 130 96 93 114 60 93 103 48 157 139 132 157 115 7261 79 64 14 31 80 130 95 140 46 131 92 74 139 5 122 75 145 14 19 121 22143 121 86 119

TABLE 6f Address of Parity Bit Accumulators (Rate 8/9 - Coded Block Size2160) 116 121 22 107 120 113 90 115 168 225 70 199 208 137 190 99 220113 34 207 52 177 94 235 204 229 66 171 100 85 218 123 16 113 2 23 96 7326 159 120 169 138 199 104 65 130 139 96 161 194 143 104 209 226 39 236125 182 79 140 13 50 79 28 193 118 188 89 34 224 61 50 128 81 46 156 9111 156 37 175 72 105 239 64 137 131 176 182 135 148 18 95 100 54 215224 174 103 165 238 87 145 214 207 89 182 55 53 38 159

TABLE 6g Address of Parity Bit Accumulators (Rate 8/9 - Coded Block Size2880) 33 174 30 142 266 282 240 78 291 229 80 43 156 132 134 303 50 31287 239 68 186 92 75 59 203 255 37 171 139 287 45 101 23 89 52 20 271 38109 84 32 111 225 183 314 101 110 142 163 44 25 206 302 173 5 86 272 1839 237 199 140 86 248 159 56 167 215 283 76 254 190 187 148 291 310 5753 99 90 134 151 199 111 30 227 148 51 167 33 294 190 147 173 84 175 10835 317 138 111 300 73 306 292 224 106 307 274 202 153 79 58 195 131 10249 242 51 9 28 275 6 287 54 246 313 106 88 49 315 42 218 265 212 239 85306 147

TABLE 6h Address of Parity Bit Accumulators (Rate 8/9 - Coded Block Size3600) 267 282 5 84 96 78 167 18 276 240 117 303 136 175 169 324 117 73360 4 379 398 265 253 146 11 62 89 114 227 342 31 26 284 295 49 239 137124 350 118 266 191 155 213 310 20 73 384 231 396 323 216 317 150 129232 58 27 245 272 18 59 253 62 376 44 337 293 392 42 396 87 270 91 25284 2 22 157 8 169 355 174 71 330 336 156 11 325 343 265 226 395 101 263163 60 152 303 250 245 206 289 382 354 57 368 212 201 271 214 120 237 1168 362 174 180 269 315 7 233 112 290 11 157 183 351 284 9 95 240 233 335261 152 78 267 348 253 42 75 78 75 29 98 64 84 385 378 54 39 152 132 29841 3 396 171 183 397 328 47 336 197 218 214 19 266 57 166 285 265 284214 75 5 239 74 46 244 313 317 127 8 3 65 50 60 177 310 119 325 136 36134 152 154 59 103 323 245 369 120 148 328 387 21 20 355 13 238 384 193154 351 121 322 390 44 66 326 39

TABLE 6i Address of Parity Bit Accumulators (Rate 8/9 - Coded Block Size4320) 30 196 79 344 162 460 169 79 210 252 30 83 389 334 100 47 199 11210 305 344 333 474 454 400 137 475 29 328 137 67 453 228 258 371 16 8268 197 38 174 403 56 41 25 52 309 303 239 152 81 379 106 452 443 31 474149 238 119 465 314 349 366 406 458 395 152 229 38 432 457 421 360 113247 244 144 178 315 189 97 212 62 375 166 356 397 2 307 79 436 385 314411 287 159 389 392 190 77 115 316 118 50 284 59 53 329 67 277 42 177466 331 380 144 335 402 52 48 449 126 151 160 273 70 143 53 440 436 321262 469 271 379 374 55 394 181 279 57 168 176 225 134 322 267 220 418203 308 270 332 257 398 82 379 104 167 117 141 82 168 119 332 470 370165 96 361 51 463 225 363 460 468 151 461 103 444 357 359 357 203 188 1350 379 385 256 274 393 123 408 434 142 96 426 414 343 22 106 277 434108 363 110 257 407 85 353 204 45 307 424 39 230 376 41 346 416 259 124

TABLE 6j Address of Parity Bit Accumulators (Rate 8/9 - Coded Block Size5760) 353 507 64 261 477 315 226 338 72 128 203 524 180 202 549 634 189460 321 307 339 402 117 164 461 342 193 78 145 236 119 63 100 365 496418 210 341 285 136 376 482 304 510 468 31 274 75 587 550 182 409 30 365461 19 184 599 351 66 28 627 2 475 143 352 175 161 163 637 166 159 33138 486 307 580 583 384 8 573 524 380 465 510 366 451 154 93 258 525 304358 286 434 410 458 26 442 565 530 385 548 99 207 142 119 321 177 529372 111 213 517 492 276 71 473 407 479 325 351 298 62 219 368 361 476 56304 558 543 554 515 527 621 379 447 56 482 560 469 205 637 453 334 18500 469 244 395 102 230 593 92 547 160 491 103 266 541 50 233 156 77 72397 39 464 305 68 284 519 307 35 281 349 44 191 275 460 296 232 348 543332 626 40 23 28 31 205 512 476 107 519 60 458 224 9 406 148 341 346 442270 544 283 259 571 503 363 157 472 425 170 107 384 425 288 467 86 199323 564 536 513 10 167 352 500 48 104 432 347 311 392 118 571 396 145584 609 328 145 50 403 181 625 159 73 169 271 265 626 552 327 564 439132 55 384 221 57 75 477 292 598 16 273 148 90 209 266 160 451 98 20 143274

In accordance with further exemplary embodiments, with further respectto the LDPC coding, the LDPC encoder systematically encodes aninformation block of size k_(ldpc), i=(0, i₀, i₁, . . . , i_(k) _(ldpc)⁻¹ into a codeword of size n_(ldpc), c=(i₀, i₁, . . . i_(k) _(ldpc) ⁻¹,p₀, p₁, . . . , p_(n) _(ldpc) _(−k) _(ldpc) ⁻¹). The transmission of thecodeword starts in the given order from i₀ and ends with p_(n) _(ldpc)_(−k) _(ldpc) ⁻¹. By way of example, the LDPC code parameters (n_(ldpc),k_(ldpc)) are denoted as follows (Table 7):

TABLE 7 LDPC Uncoded LDPC Coded Block Length Block Length Code Ratek_(ldpc) n_(ldpc) ¼ 16200 64800 ⅓ 21600 64800 ⅖ 25920 64800 ½ 3240064800 ⅗ 38880 64800 ⅔ 43200 64800 ¾ 48600 64800 ⅘ 51840 64800 ⅚ 5400064800 8/9 57600 64800   9/10 58320 64800

The task of the LDPC encoder is to determine n_(ldpc)−k_(ldpc) paritybits (p₀, p₁, . . . , p_(n) _(ldpc) _(−k) _(ldpc) ⁻¹) for every block ofk_(ldpc) information bits (i₀, i₁, . . . , i_(k) _(ldpc) ⁻¹). Forexample, the LDPC encoding process can be summarized as follows:

(1) Initialize the parity bit accumulators a₀=a₁= . . . =a_(n) _(ldpc)_(−k) _(ldpc) ⁻¹=0;

(2) For the first information bit i₀, accumulate i₀ at the respectiveparity bit accumulators according to the accumulator addresses specifiedin the first row of the table for the respective code rate and blocksize (n_(ldpc))—For example, Tables 8a through 8k (below). For example,for rate 9/10 (Table 8a, below), the following operations are performed:a ₄₀₅ =a ₄₀₅ ⊕i ₀a ₃₃₄₂ =a ₃₃₄₂ ⊕i ₀a ₃₆₆₄ =a ₃₆₆₄ ⊕i ₀a ₆₂₇₈ =a ₆₂₇₈ ⊕i ₀

-   -   (where all additions are in GF (2)).

(3) For the next M−1 information bits i_(m), (m=1, 2, . . . , M−1),accumulate the information bits at the respective parity bitaccumulators according to the accumulator addresses

${\{ {x + {m\mspace{14mu}{mod}\mspace{14mu} M}} \} - {\{ {\frac{x + {m\mspace{14mu}{mod}\mspace{14mu} M}}{M} - \frac{x}{M}} \}*M}},$where (a) x denotes the address of the parity bit accumulatorcorresponding to the first bit i₀, (b) M is the number of columns of arespective edge RAM (e.g., 360), and

$q = {\frac{n_{ldpc} - k_{ldpc}}{M}.}$Here also, within the brackets { } of the second term of the foregoingformula for determining the accumulator addresses, the division for eachterm

$( {{that}\mspace{14mu}{is}{\mspace{11mu}\;}\frac{x + {m\mspace{14mu}{mod}\mspace{14mu} M}}{M}\mspace{14mu}{and}\mspace{14mu}\frac{x}{M}} )$reflects integer division. Continuing with the rate 9/10 example (Table8a), with M=360, for information bit i₁, the following operations areperformed:a ₄₀₆ =a ₄₀₆ ⊕i ₁a ₃₃₄₃ =a ₃₃₄₃ ⊕i ₁a ₃₆₆₅ =a ₃₆₆₅ ⊕i ₁a ₆₂₇₉ =a ₆₂₇₉ ⊕i ₁

-   -   (where all additions are in GF(2)).

(4) For the (M+1)^(st) information bit i_(M), accumulate i_(M) at therespective parity bit accumulators according to the accumulatoraddresses specified in the second row of the respective parity bitaccumulator address table. Then, in a similar manner as in (3), for thenext M−1 information bits i_(m), (m=M+1, M+2, . . . , 2M−1), accumulatethe information bits at the respective parity bit accumulators accordingto the addresses

${\{ {x + {m\mspace{14mu}{mod}\mspace{14mu} M}} \} - {\{ {\frac{x + {m\mspace{14mu}{mod}\mspace{14mu} M}}{M} - \frac{x}{M}} \}*M}},$where x denotes the address of the parity bit accumulator correspondingto the information bit i_(M) (e.g., based on the entries in the secondrow of the respective parity bit accumulator address table). Here also,within the brackets { } of the second term of the foregoing formula fordetermining the accumulator addresses, the division for each term

$( {{that}\mspace{14mu}{is}{\mspace{11mu}\;}\frac{x + {m\mspace{14mu}{mod}\mspace{14mu} M}}{M}\mspace{14mu}{and}\mspace{14mu}\frac{x}{M}} )$reflects integer division.

(5) In a similar manner, for every group of M new information bits,accumulate the information bits at the respective parity accumulatorsbased on accumulator addresses obtained from a new row of the respectiveParity bit accumulator address table and the formula

$\{ {x + {m\mspace{14mu}{mod}\mspace{14mu} M}} \} - {\{ {\frac{x + {m\mspace{14mu}{mod}\mspace{14mu} M}}{M} - \frac{x}{M}} \}*{M.}}$

(6) After all of the information (input) bits are exhausted, startingwith M=1, sequentially perform the following operations (e.g., layeredbelief operations or a layered belief algorithm for a layered beliefdecoding mode) with respect to the parity bit accumulators a_(i):

$\begin{matrix}{a_{M} = {a_{M} \oplus p_{0}}} \\{a_{2M} = {a_{2M} \oplus a_{M}}} \\{a_{3M} = {a_{3M} \oplus a_{2M}}}\end{matrix}$ ⋮      ⋮     ⋮ $\begin{matrix}{a_{n_{ldpc} - k_{ldpc} - M} = {a_{n_{ldpc} - k_{ldpc} - M} \oplus}} & {a_{n_{ldpc} - k_{ldpc} - {2M}}\;}\end{matrix}$ ⋮          ⋮            ⋮a₁ = a₁ ⊕ a_(n_(ldpc) − k_(ldpc) − M) a_(M + 1) = a_(M + 1) ⊕ a₁a_(2M + 1) = a_(2M + 1) ⊕ a_(M + 1)    ⋮       ⋮      ⋮ $\begin{matrix}{a_{n_{ldpc} - k_{ldpc} - M + 1} = {a_{n_{ldpc} - k_{ldpc} - M + 1} \oplus}} & {a_{n_{ldpc} - k_{ldpc} - {2M} + 1}\;}\end{matrix}$ ⋮          ⋮            ⋮a₂ = a₂ ⊕ a_(n_(ldpc) − k_(ldpc) − M + 1) a_(M + 2) = a_(M + 2) ⊕ a₂a_(2M + 2) = a_(2M + 2) ⊕ a_(M + 2)    ⋮       ⋮      ⋮ $\begin{matrix}{a_{n_{ldpc} - k_{ldpc} - M + 2} = {a_{n_{ldpc} - k_{ldpc} - M + 2} \oplus}} & {a_{n_{ldpc} - k_{ldpc} - {2M} + 2}\;}\end{matrix}$ ⋮          ⋮            ⋮a₃ = a₃ ⊕ a_(n_(ldpc) − k_(ldpc) − M + 2) a_(M + 3) = a_(M + 3) ⊕ a₃a_(2M + 3) = a_(2M + 3) ⊕ a_(M + 3)    ⋮       ⋮      ⋮ $\begin{matrix}{a_{n_{ldpc} - k_{ldpc} - M + 3} = {a_{n_{ldpc} - k_{ldpc} - M + 3} \oplus}} & {a_{n_{ldpc} - k_{ldpc} - {2M} + 3}\;}\end{matrix}$ ⋮          ⋮            ⋮ $\begin{matrix}{a_{M - 1} = {a_{M - 1} \oplus a_{n_{ldpc} - k_{ldpc} - 2}}} \\{a_{{2M} - 1} = {a_{{2M} - 2} \oplus a_{M - 1}}} \\{a_{{3M} - 1} = {a_{{3M} - 1} \oplus a_{{2M} - 1}}}\end{matrix}$ ⋮      ⋮     ⋮ $\begin{matrix}{a_{n_{ldpc} - k_{ldpc} - 1} = {a_{n_{ldpc} - k_{ldpc} - 1} \oplus}} & {a_{n_{ldpc} - k_{ldpc} - M - 1}\;}\end{matrix}$

(7) The final content of the parity bits p_(i) of the codeword c=(i₀,i₁, . . . i_(k) _(ldpc) ⁻¹, p₀, p₁, . . . p_(n) _(ldpc) _(−k) _(ldpc)⁻¹) are reflected by the resulting parity bit accumulators a_(i), (i=0,1, . . . , n_(ldpc)−k_(ldpc)−1).

TABLE 8a Address of Parity Bit Accumulators (Rate 9/10) 405 3342 36646278 121 538 4579 4801 776 3102 3279 5298 135 1119 4225 6307 440 9023893 5464 139 3289 5101 5543 1016 1893 3076 5942 2253 2759 5611 6055 3351122 3260 5610 436 2337 2781 4648 2027 2451 5009 5137 1165 2440 43316125 1704 1858 3986 5327 938 2077 3080 5007 1239 1668 4309 4524 14642825 3640 4979 1682 3716 4081 5851 2709 2976 5931 6213 3811 5917 63421558 3818 4076 2290 5606 5807 2080 2467 4655 465 2866 4971 873 1881 46241301 2270 5161 1637 2567 4787 1380 4475 5563 258 2769 3845 240 1228 338746 5258 6393 583 1652 4139 2983 4137 5095 601 3064 3299 1821 6025 6123775 3243 5674 822 3142 4768 3068 3255 6474 1006 2795 4896 2791 2997 59092583 3167 6427 1395 4398 5579 608 2248 3277 2491 5104 5580 2437 42284444 246 568 3849 253 3723 4093 242 3968 6360 700 964 4904 1470 47145146 866 1382 3801 1107 3368 4559 1679 1981 6041 1868 5706 6063 16021894 5142 289 2726 4941 1943 3179 6347 2186 4446 5537 1055 3361 5448 5312627 4448 1467 3414 5117 1738 4095 4628 1254 4214 5078 2218 5681 5936272 5085 6284 139 1218 6269 576 3127 4258 1122 3584 3844 1795 4712 60921071 3754 4913 728 1868 3004 586 2425 2573 1986 3826 5894 217 1148 41231136 3201 3286 1138 4906 5344 548 3705 6148 2510 3974 4654 1846 29495959 2374 4890 6009 1495 2556 4359 582 4226 4406 233 3425 3922 1017 37345431 2358 5105 6251 260 418 2567 1627 2737 5360 788 3492 5646 1561 20574812 2147 5844 6217 952 2938 5458 1468 1837 4577 234 5186 6359 372 25052680 112 461 3311 1294 3488 6350 1377 2441 6280 841 2776 5751 295 25915086 1628 4822 5080 3920 5608 5788 641 3885 4916 1482 3689 5845 29303257 5936 750 4659 4733 1864 2899 4301 1068 1963 5753 2214 4295 46501367 3170 4306 1519 4107 5104 289 4410 4959 1252 5166 6162 389 1624 44221420 1543 4360 669 3321 3631 125 1396 3536 2955 5317 6367 561 2194 41272206 4179 6352 794 3549 5771 2570 3692 4924 2001 3095 4990 2380 56386039 733 2805 3687 2704 3062 6013 187 2154 5745 861 1833 5750 1197 23124677 941 2008 4171 994 4565 5542 2058 3148 5976 789 1130 5079 448 45314763 1082 3375 5742 3455 5065 5744 621 1691 4313 90 4103 5953 1592 32663800 3144 5789 6418 270 2561 3650 668 2477 6348 2011 3060 4880 1490 38864777 122 2583 6348 2484 2643 5308 714 3867 4171 192 2798 3938 2420 47336067 647 1656 3776 85 6080 6232 1058 3109 4875 3035 3305 5118 1711 42166044 918 2044 4085 458 2522 4675 1113 2240 6268 1686 2087 5113 2385 27736280 1405 3216 5737 2016 4555 4733 853 3414 4395 3344 5214 5751 306 11535579

TABLE 8b Address of Parity Bit Accumulators (Rate 8/9) 185 1982 50906885 2051 2208 6645 7139 463 930 3108 5287 267 4014 6164 6820 1118 16293252 5478 1939 2411 4705 6527 3131 3252 5283 6315 1376 4003 5928 68751744 2522 4828 5888 775 1312 4686 6012 1147 2917 5313 5516 1657 28523653 6751 2580 3234 5634 5767 2344 2721 4417 6418 179 3305 3726 7140 2653322 4581 6309 443 2495 4394 4866 437 1796 3762 4139 768 1957 3793 3966647 892 4421 5589 990 2583 2887 4756 1066 1924 3116 6195 1993 3020 53755699 2781 4456 6173 6700 1280 1782 3254 5823 1102 1476 3325 5079 7171636 5021 5053 718 1445 2691 5432 1965 3073 5711 6010 1941 2496 48026018 2517 3299 5556 6486 825 3944 5793 6425 666 2499 2522 4531 287 6193347 3816 964 1328 4743 5169 1157 2369 4523 7043 127 4266 4568 6180 3073640 4260 6893 292 4052 6794 7117 3713 4114 6485 7015 916 1840 4808 5220139 438 3527 4645 654 1723 3612 4033 47 4410 4716 7198 1432 3782 41266347 41 1835 4267 5105 228 4313 5213 6963 894 3161 4884 5093 1561 28143746 6634 1393 1792 5407 5863 685 1078 2679 3088 1529 1937 5427 57811056 3146 4779 6602 649 2204 2568 6951 2768 3151 5521 6676 2074 24845833 6967 2398 3331 4515 5561 1280 3728 5934 6182 2485 3373 6190 68151141 3276 4393 6389 104 3339 7107 656 3450 5083 1912 3649 7037 273 21196733 916 4161 4570 2206 4605 6266 2610 3601 5771 723 1363 3961 2300 27906200 4199 4441 6771 1495 2820 5471 936 1329 5098 1475 5488 6486 11853676 4992 2330 5321 6307 2004 2901 5853 3133 3465 5656 120 4787 5879 3841757 4790 701 2989 6954 193 3359 3727 1352 3685 4958 1982 2227 5529 18413055 6728 225 498 6919 2731 4716 6809 1503 2052 5524 1234 3886 5007 13414384 7124 434 868 6365 2928 5292 5711 2569 4525 7013 2659 3072 6131 541995 5083 202 4311 5089 2258 6221 6630 1715 4295 6096 2435 4296 4435 9003540 5913 1671 3425 5981 1627 2049 5389 1946 3883 4259 1194 3432 60181903 6028 7168 67 3683 6193 2604 3891 5706 216 4278 4516 908 2717 54972309 4658 6455 1338 4593 6133 2279 5039 6588 334 4056 5129 3244 54606040 685 5104 6933 1369 2978 5006 2318 4819 7028 639 809 3032 585 15472797 966 3231 6705 1573 3363 6546 2085 6713 7136 1171 3970 5141 249 27694607 1519 4336 4827 377 1688 5622 3204 4717 6716 576 1078 3713 4697 57657128 1933 5226 6382 708 1625 2782 3166 5564 6505 808 2529 5679 64 11073749 1971 3071 4053 2298 4369 6479 1255 3962 5119 2359 5902 6978 1693333 3750 739 3475 6479 2380 3302 6020 1153 2982 6933 108 3675 4989 16843397 4607 2468 3309 5749 1567 3494 5287 2695 5500 6779 1650 3987 5381952 3655 5634 931 4061 5859 1862 3208 5942 114 1175 4355 59 3906 64521337 4180 7050 1052 2851 5200 2014 3149 6787 662 2573 4810 2249 60256192 1868 2250 6544 702 5004 6942 488 4582 6161

TABLE 8c Address of Parity Bit Accumulators (Rate ⅚) 798 1195 3207 35565147 5412 7636 8021 181 3530 5203 5661 7617 8048 10135 10609 1462 18983635 3961 6209 6648 8552 9391 761 2127 2918 5450 7539 7636 9676 98091878 2332 5152 5494 7238 7765 9607 9727 181 3351 5105 5496 7409 77029598 10763 433 2788 3838 5588 5828 7800 8720 9731 488 2907 3472 63276569 8352 8930 10689 89 2842 5508 6026 7669 8121 10349 10699 1925 22314325 5010 6583 7643 8721 9846 1073 1231 3228 4187 5319 6420 7491 8521154 2531 4592 5601 7458 7695 10201 10581 479 881 2553 5231 5431 78478862 9787 391 818 3787 4243 5817 7830 8104 10055 97 588 2769 3729 59736278 8902 9993 2045 2185 4299 6169 6816 8287 8827 10767 507 1663 27293810 4901 5789 7930 9212 2496 2802 4651 5027 6717 7163 9596 10444 1592056 4328 4854 6630 8590 9452 10469 105 1425 3252 3895 5416 6726 92049691 518 2749 3784 4758 5853 6843 8190 10706 331 2785 4978 5396 71628264 9814 10120 418 2240 2800 4818 6481 7079 8751 10595 1066 2927 41305387 6921 8198 9866 10247 25 3567 3892 5833 6308 7967 8287 10482 54 6792617 4622 4734 6949 8644 9208 214 525 4266 4365 6258 6756 8899 9914 20302273 4200 4413 6808 6929 9081 10322 810 1196 3735 4282 6022 6390 88119881 869 3411 3871 5997 7129 8067 9328 10212 833 7114 8123 432 2458 41081764 7069 9592 4174 5900 7187 2292 5716 8280 2941 4153 5310 3285 39186052 794 3044 8493 1528 2043 4966 2117 9315 10277 1191 2175 6178 14695270 7449 1107 1504 6235 2293 4650 6746 839 4508 9493 1715 5088 89313454 4487 9120 2059 7336 9626 3162 4847 8433 3098 9173 9491 3195 631710336 1402 2396 7200 1190 4378 7312 3132 3499 10186 1505 1947 10088 13563312 9270 4853 7227 8577 1760 7218 9050 1124 1500 9030 1133 1501 84841277 2932 10769 369 6143 7263 2624 4740 8068 2270 5183 10587 1490 52785741 2996 5955 10051 2646 5143 7804 3515 5866 9203 2007 4063 7813 27846381 6663 1535 4845 8402 2345 6141 9480 7229 9659 10068 5821 8323 8658388 5608 7239 4440 5599 8039 3254 3863 10116 145 4960 9463 4161 65336951 854 7196 8816 4022 7710 10676 1111 2194 8266 627 3218 3319 18844623 8735 1904 6509 9830 898 1433 3632 788 3712 8292 1668 7197 9130 3304454 10156 244 9082 10160 2683 3844 4759 1266 1752 5956 781 5063 103341256 1626 4876 1758 7765 8001 980 3659 7851 4149 8190 10202 92 3468 5352825 5942 7041 3015 7100 10738 3478 5859 8168 3629 9571 9750 5503 68188354 3328 7496 10540 169 4810 9788 4408 5712 6625 1988 5507 9347 4615210 8677 263 4203 8549 4588 7551 9631 2122 2239 8785 6645 9519 106242312 4343 8735 2199 4041 7078 1817 7474 8339 2908 6305 9881 3070 907710184 1137 6336 9262 437 2562 7750 671 2647 6444 3094 5542 5834 24984042 7138 3933 8184 8378 769 2671 9268 425 3579 5432 4120 4369 8476 5463291 5723 2273 2530 7559 425 1494 5071 275 1890 9065 4492 5010 10023 1471404 5990 4047 9339 10134 5177 7388 9568 2151 7534 10210 191 2601 63671124 3094 9452 1405 7140 9375 3908 9782 10082 1902 4924 8442 1706 43236831 1786 3732 6867 7563 8939 10016 5784 8885 10703 6173 8155 10542 30114950 7607 3283 8830 10655 895 5348 8081 2444 6732 7821 750 6367 6530

TABLE 8d Address of Parity Bit Accumulators (Rate ⅘) 498 2356 3399 46315536 7415 9550 9825 11986 499 722 3381 4400 7825 8864 9980 10902 12000923 1278 3976 5353 6383 7233 9807 11841 12067 1027 1141 3080 3450 62706615 8936 10053 12197 241 641 2589 3938 5948 7939 8405 10918 12913 11401748 3891 3977 5929 6450 8852 11141 11465 389 720 2956 3508 5292 63907424 9013 11890 913 2029 3157 6116 6139 8615 9640 10504 12410 1169 23563348 5141 5417 8732 9775 10888 11893 2068 2926 4223 6046 7006 9224 965112316 12691 1872 2497 4581 6490 8352 8820 10713 10983 12827 883 13382907 3415 6435 7383 9426 9937 11822 2638 2906 5312 5413 8136 9226 1011712244 12602 223 2800 4527 5538 6773 9346 9604 11204 12275 277 2712 38925465 5996 7851 10705 11551 12726 2053 2383 4042 4524 6654 7155 9091 938111287 1645 2733 3773 4901 5829 8913 9297 11284 12363 596 1703 2826 46574790 7024 7407 10286 10768 1260 7640 10440 413 1758 7516 6709 6900 110711638 11242 12568 247 4966 8252 2125 3685 7002 252 10234 11279 17 19215116 2515 4974 7892 2470 8033 12635 8169 10285 10536 7131 7997 117311646 4100 6581 5489 8335 10367 4315 5206 7834 3661 8534 10114 4825 853711665 4735 7855 11729 3636 7050 12359 5855 11577 12216 3709 4041 119741302 4819 9598 3726 5951 12780 439 6839 12862 6107 6862 10014 329 34009601 4365 4963 6828 2659 10871 12147 2956 5165 12608 1292 3562 8246 16949213 10369 558 1639 7845 5331 8084 10216 4385 4729 6706 5253 5424 11744718 1662 8953 8672 9013 10984 3992 4522 9006 1971 3055 6477 6282 75429563 3542 10674 12427 2869 8558 8790 2382 7955 11422 2227 5687 109177260 10148 11466 866 2025 6459 807 8584 11291 3185 5589 8581 724 421310711 6951 7549 12599 2034 2386 10704 306 2866 11776 1115 7630 9974 2267681 10061 1262 8047 11342 2579 11466 11672 5616 5900 9675 214 525 101892502 4013 9398 4192 8827 11901 749 8020 11632 2689 10394 12856 45 333112206 1852 3988 10681 1080 8893 11333 2708 11688 12168 144 4672 102896772 7703 8784 562 733 7714 768 5510 9791 519 9482 10071 1462 5139 91181443 2000 4859 1636 3443 6279 2989 3370 5667 5155 6176 7256 2052 52617773 2950 8290 11050 5767 6931 7984 4358 6356 10596 2486 10860 129191421 3168 9846 5989 8551 10654 4504 4762 12565 4925 6522 10829 7308 850312839 2383 7034 7547 3957 9245 12567 3857 9346 12337 3692 6689 6950 30844828 7816 977 3692 6597 1538 7007 9577 623 8432 10784 6408 7355 10231946 9879 12496 7515 8521 10900 4040 8421 10792 3361 5178 6908 2236 873510552 3647 6779 9745 5516 6702 12914 272 11360 11827 1847 4653 12103 257344 9583 2454 11437 12443 2047 4203 6137 6285 10091 11506 3281 46569090 4289 8798 12488 1220 9341 10946 73 3759 7981 6859 8176 10167 17554703 5322 1434 10905 12144 2380 3454 8174 1259 11673 12041 408 485212932 3116 5666 7879 2986 8641 10037 1022 6055 11595 1604 5858 7579 18605406 12830 2547 5839 9415 454 2602 4342 2697 5238 9006

TABLE 8e Address of Parity Bit Accumulators (Rate ¾) 755 3136 3253 55418180 13010 14277 15226 464 989 2773 3063 5246 5711 7829 10703 687 21745068 6955 8933 9180 12238 12247 620 868 3613 7063 7491 9977 11659 122311121 3221 3985 7303 8598 9677 11994 15459 239 3514 3734 5618 7483 944313290 14309 624 1641 4395 4791 8232 8520 11653 13714 1764 3468 3630 68838179 10354 10666 12589 5441 6021 9211 10116 11365 12476 15587 16031 11913709 4945 5821 9932 13549 13712 15675 4312 4559 6892 9729 11121 1284714493 15725 2522 4963 7683 8080 10332 10545 13579 15279 2324 2660 465010336 12099 12402 14149 14535 6217 6529 9102 11077 11401 13051 1424716145 1900 4014 6973 9765 10139 13297 15029 15931 356 3856 4735 819710020 13408 13819 16041 589 3148 4079 5870 6141 9278 11221 11732 31625352 6442 7233 8287 11507 13756 15666 1600 8280 14758 8404 8921 132481796 8643 13329 3470 5959 10511 1771 2651 10918 5690 14326 14698 49697444 13930 3426 9264 13439 6079 7897 12750 731 5131 12199 4567 945315026 804 12393 12657 1363 2349 15827 2393 5056 11552 183 11487 15154 331989 15052 352 2157 14479 2459 2678 11725 7572 8993 11156 4590 1050110934 3970 6836 16007 6430 6525 9597 2015 12757 14985 1842 6677 769212934 14875 15425 1165 6320 9437 1205 6831 8927 3986 8773 15795 73108501 14143 5813 10378 10472 3293 12137 15600 750 6051 8898 7955 1359516006 947 6895 16179 1474 5536 11069 214 1979 5872 1373 1461 13091 811612210 15540 188 2677 6413 2785 6824 14251 2798 8431 12629 470 1655 38724471 6408 8522 8263 11449 16194 9329 9687 11535 21 6478 13326 2904 714111399 701 7076 11584 3166 5197 15397 5328 5731 7774 875 12344 15421 917713008 14984 3884 7246 14544 3334 6747 10089 4492 10028 13128 2463 1243114331 2429 11404 14714 4661 11689 15261 6515 12787 14813 3354 9539 98579146 12412 12863 585 4001 7578 2300 7776 13341 3839 4001 14733 7541 982715058 5177 10853 12062 4861 10697 11004 1976 4984 9453 1118 10773 139501800 2888 4942 5525 10278 13858 1141 8799 14032 5552 8722 11930 375510366 15563 3879 6873 9914 1236 10327 13474 10007 12774 15695 2178 904716151 6256 7420 11075 7780 12124 14020 5611 7207 15439 2529 4322 150872714 5217 9884 81 10799 11594 1845 7854 12328 2480 4360 8883 1107 699110377 3479 5761 14289 5639 8855 9053 1460 3703 11295 7710 12577 143754720 12673 14956 1176 12155 13882 2187 6857 12985 1622 5874 9437 9422765 14378 3492 5768 12701 6432 14722 14794 11046 13036 15948 2904 42117521 229 592 4897 1616 8035 11683 10569 13395 14431 4474 6712 1515813340 13920 15592 5030 13245 15131 1061 6169 6794 328 6771 12242 839810475 10827 535 5368 9184 1903 5121 11454 745 2003 14697 503 3281 114353200 8219 8491 8299 9504 11601 4128 8160 16124 2994 4032 9680

TABLE 8f Address of Parity Bit Accumulators (Rate ⅔) 1615 2039 820011116 12879 13266 14888 1056 2837 5958 7722 10531 13028 16131 321 41966772 8327 18370 21171 21440 2720 4996 7486 11437 15927 16234 21032 2504778 5126 9839 16614 18590 21299 36 10862 13201 15758 17702 20512 213104548 8263 11202 12249 14424 17146 20605 521 2272 5846 7080 11967 1564217973 1858 5497 5858 7892 13057 15657 19262 65 1964 3694 6305 7236 1292414509 648 3736 6461 10779 13755 17583 19163 4991 6081 9123 11807 1214418877 20967 667 1787 6412 8270 13080 15684 19871 7185 7366 14404 1701117561 19430 21050 2701 4406 9153 9479 15365 19423 21462 3942 7315 1093314239 17054 17558 19977 1427 5839 8022 10208 16873 16924 21529 60 64597405 9609 11824 16053 19264 1956 4737 6790 9007 12579 16313 19839 69498003 10138 12354 14675 17960 20107 3267 6813 10410 12761 14996 1515117838 975 1375 3246 6456 9683 9895 14572 496 4250 9354 10365 14249 1672419585 4187 5342 7802 10016 10840 13690 14811 954 9023 12299 15481 1730819923 20256 1554 2755 4407 4842 10638 16587 17877 1953 3616 8712 1220614211 16877 21233 1295 4174 4522 9604 12613 14892 17298 500 3106 533412580 12669 15443 18409 2283 8824 9896 13581 13889 20424 20765 1332116111 18888 6938 17206 19746 1784 4153 15066 9407 14334 18336 5350 694210093 3170 8370 11789 905 1308 8307 3052 5479 14093 1269 16063 194422686 4519 8777 1756 3659 11721 3002 11645 18023 8978 10622 20164 884611139 13721 3066 10762 13957 3464 11167 13550 16215 18615 18961 767615415 18065 5396 10017 18358 7850 16492 18269 3531 16286 18989 573911192 13524 1009 18408 18920 6625 13662 15264 3505 12215 20200 842612029 20522 8496 19529 20705 2218 6541 11495 2253 5667 20631 2320 573919782 2335 8137 9814 1688 9285 15288 1393 8162 12727 3355 11661 14163142 10231 20568 9158 12878 13257 14324 17954 19658 2483 4417 18250 66110219 14001 6896 10200 14537 8802 17982 20021 2787 9042 14255 3101 1318018975 1164 8420 16306 6500 9735 12804 11842 14862 19904 7598 8199 179104273 17028 20983 544 9997 17358 3136 19586 20591 1785 5171 9714 838814782 18328 32 6240 10995 865 5080 8797 624 11476 14648 2163 7348 13686101 3574 18935 7330 13508 14000 5743 7379 9514 1592 11437 17432 48936775 20933 762 2691 7070 3030 19170 20360 4299 7845 19138 1978 658912314 2757 11178 14780 4956 5881 21471 3392 7590 19773 15990 19435 202271888 5932 16298 4085 5882 12449 4813 16665 20934 5522 9375 18435 1046612470 16771 11805 16606 21277 856 5550 18431 1094 12130 15534 1454917123 19074 5076 13100 17343 10615 16455 20767 13544 15381 16991 382918367 21333 15456 15532 19920 6866 15766 18286 6461 8677 12234 202612038 20327 3839 8318 10649 4613 11022 15972 3757 13434 15910 4519 646111133

TABLE 8g Address of Parity Bit Accumulators (Rate ⅗) 487 2424 5103 629414728 16989 22394 22707 1634 5235 7897 8219 10473 10926 15226 17159 78368222 10026 12421 17812 20194 21551 25762 178 4183 5238 8916 11565 1351317234 23622 2619 3761 6539 10279 11943 16294 19745 22819 1097 3310 529710950 12939 13749 18284 19985 5062 8675 11402 13351 14655 16741 2055322461 5862 7897 12406 13503 16929 17631 20389 22142 1160 8004 9813 1354014666 18003 22246 24879 157 6179 13015 16673 17089 19482 23223 243241568 3396 5983 13072 13336 18349 18521 21010 3632 5935 7011 12522 1585717935 18950 23596 7555 8375 10646 12391 15071 20478 22501 23402 20002378 7387 11854 13513 21598 24971 25503 476 2578 7339 8402 13753 1614719513 22512 1646 7593 8714 9846 12535 14403 21897 22723 913 3205 53846134 13821 16335 23236 24236 502 1494 5665 8092 9094 13273 18152 238563571 5849 7970 10318 16538 19009 19186 24775 1768 5020 10749 15104 1844621191 21392 25505 279 7272 9982 10336 13151 15451 18316 22103 2005 40264677 7991 9235 13384 14754 23731 1319 3499 6567 7679 11063 15094 1526717449 6162 6797 10759 11683 12866 13911 17226 22718 2382 9187 1180816423 18162 19122 21873 22911 216 1114 7075 14485 16966 19607 2291424691 721 2693 6387 8821 17550 19330 22719 24673 972 2842 8828 993312899 15009 15268 23746 1947 4539 10078 12725 13876 18387 20589 247831755 4300 6903 8799 14179 14485 20595 24429 3854 4896 7018 10751 1401614346 16861 19163 3859 4085 5919 7733 15182 16468 19409 21431 1371 676310705 10999 14233 17684 21160 22018 2356 5185 5651 12200 12308 1638418868 21030 6600 8655 9801 11712 13854 16725 20795 25380 1692 3627 69627462 10218 21056 21314 24003 16314 19603 22678 1179 19957 21941 1416319047 24512 10474 20933 24258 461 8308 11535 7361 11441 12375 40 641710855 6001 22526 23757 1071 3964 9467 2756 6525 23536 449 3246 1178212053 19545 21812 2670 3701 10363 7809 17817 20062 2900 6138 24663 70429061 22324 7149 12133 15790 7464 15848 22261 4406 15275 21965 2305 824015658 844 3405 18366 1893 2451 17338 5810 17934 20992 2244 4845 2415817878 18964 23878 5429 22314 24712 303 14398 24478 15836 18743 218264587 17442 23891 9067 19984 25568 12659 20803 25727 5409 6673 23824 969215061 18694 861 1169 16870 12226 14993 20284 13054 14784 20185 160 1550123163 614 18992 23847 4719 15363 20481 19129 23171 24212 5465 2165025118 3669 15823 17361 12767 13112 21339 4658 14270 17975 503 1129614239 16728 20243 25123 1952 12991 19964 11201 17284 18410 2840 1287724940 4989 21344 23127 3268 15681 23795 2050 16692 25423 4144 9210 10293896 8604 15852 9235 23106 25062 4425 5548 25280 4343 10845 11308 32249603 25270 1859 10301 21895 4944 11025 23373 5530 9419 25244 8525 1589618435 8591 19838 24964 18261 19436 25885 4301 15776 15875 9532 1615820694 9674 11995 20018 8382 9360 12086 2974 19579 25776 2968 4956 207853009 11349 25614 2975 11230 25789

TABLE 8h Address of Parity Bit Accumulators (Rate ½) 1690 4392 724310123 12751 19068 23261 25882 25950 4295 8310 13735 14903 18216 1852120457 22873 26999 2900 6292 14253 16327 19561 21463 23348 26738 311081201 2187 4037 6084 7112 17403 20499 23973 29486 1913 5146 8684 1076211063 15735 19611 22881 27218 1569 1918 5946 8361 9717 12102 16573 1918728309 925 7530 10304 16459 18002 20820 22693 24097 30913 4336 1431516734 16940 19494 19977 21895 25121 31768 3367 3872 10516 11797 1608018647 21646 24129 31143 1557 4179 6997 9985 19179 23292 24350 2683428821 2605 4611 6484 13227 16750 22762 26200 28877 31731 3139 6378 79439983 10171 14917 17887 19560 25630 5706 5916 8409 10080 13664 1375320142 22989 29228 4479 7229 10272 12943 17716 21870 24521 29638 32330818 2084 5177 9571 10713 14061 27997 28946 31914 4223 8466 15465 1624118591 20686 25672 28312 31533 3049 3335 8311 11572 17578 22419 2372427334 27454 607 4010 11542 13746 16393 19392 21126 28048 28409 1687 20904816 6641 7824 8909 10871 25465 30399 1282 3011 6333 8010 10952 1695824124 26242 32302 2156 4900 6829 9255 15769 16823 25927 30541 30839 31335074 7609 10078 13090 15951 22294 27409 28021 588 1624 7313 9206 1290815670 21180 22034 30955 3342 7385 7790 11060 13010 17437 21755 2805228308 3431 5338 15158 18950 23091 24334 26495 28510 30791 515 3366 1186015866 18097 19816 20516 23868 32139 219 6739 12840 20551 23331 2353025670 28997 32168 152 1161 11055 18106 18657 20617 25241 26437 306924846 9453 14029 14862 20321 22192 26263 26518 29656 3613 6463 1222915428 17644 19554 20150 27965 31614 110 6876 9265 14936 18681 31853 366116313 30499 271 6718 20110 21531 29984 30553 1164 17609 23628 8154 1338224492 3653 10000 31610 2337 21448 28080 11999 15213 25875 12821 3128631518 6097 17194 24909 9702 24304 28525 5883 18252 26861 16032 1783420825 8986 16741 21021 568 27281 27400 13853 15558 19265 1005 5259 1224310050 23589 27597 758 7779 12074 2783 12248 14536 810 1354 27229 636220993 27191 10553 18772 30110 2402 2835 21129 12261 15601 22445 1144215365 22496 9669 16977 21706 5711 13362 23591 17344 21970 29298 24013300 29750 12151 27394 32351 2346 25180 25427 2473 16162 20178 37727888 29067 4813 22325 26724 5566 11255 14096 11274 26442 28451 573314961 21477 9204 11769 32017 4994 8043 9090 5419 10606 24702 7182 1124314543 13457 24507 29332 7082 21960 26549 13422 17659 31308 4351 3002630998 11180 13085 17157 18933 21543 23781 14066 18961 22375 8255 1238819309 2529 12598 29636 8811 28673 31573 8938 24504 30413 14629 2490630234 14478 24007 30182 2559 14678 29540 25088 25451 28782 553 2550729461

TABLE 8i Address of Parity Bit Accumulators (Rate ⅖) 4173 6386 681315139 16380 22095 22454 24964 26820 27326 30289 32188 826 1264 3864 77789667 17876 20474 21361 24378 24599 28142 33137 229 1256 4395 6290 666415376 17436 19340 19463 28818 33008 36039 3801 8483 10585 12292 1341814753 17085 18901 21746 22945 35570 37330 1056 7871 8934 9916 1213117573 20277 23395 30197 33313 35985 37827 367 6393 7261 12313 1695618789 19865 22650 23639 24535 31056 36744 4276 10788 13433 16512 1738420031 26177 27799 29564 30931 33354 37567 1446 3707 5576 7649 9769 1172315461 19981 23591 30056 34358 36599 4336 4879 6768 8836 11153 1616318737 26233 28194 29209 32440 36228 4993 6006 9212 11740 14173 1652624459 25254 29745 33408 36055 36434 664 2361 9581 15385 18970 2068322481 25313 25573 28771 29109 38646 60 4096 7203 9634 13663 17240 2206922446 25032 35038 36150 37117 531 2834 6551 13051 17419 18553 2146423928 26936 29707 32040 37070 1518 2753 6081 6875 9167 10435 12956 2011723116 24850 32134 38490 3408 7120 7440 10653 12980 16264 21753 2801029934 31090 32798 37138 1625 2003 12165 12307 18588 19634 22220 2404724332 32481 32815 36389 43 5869 9888 13215 14897 16193 17231 19751 2840334240 37503 37977 995 8360 11257 11794 14564 20565 24887 27011 2937231511 36783 37169 1807 2320 5317 5423 14505 18577 20893 27636 3086533909 37026 38577 2917 3575 8016 11563 15569 17766 20889 24069 2434135063 38343 38694 127 2839 6382 9940 11027 12217 14285 27540 27894 3119931358 34474 1933 4300 6891 13497 16865 20989 22027 28776 29073 3224833905 38280 1378 3266 8115 10258 14509 21738 25522 25610 28824 2936231876 33896 849 7607 10285 10474 12436 16182 19495 21673 29264 3270635784 38261 18317 32445 34841 3016 3492 27531 11220 27356 31589 1421319144 37905 17819 20378 21592 25822 27680 28748 11051 18497 31183 875922683 30156 8604 15941 32844 19298 23156 30575 21482 28103 37945 21425436 35950 2977 10390 20959 1436 7104 12063 14316 22841 36453 4795 1510725769 4674 5422 31791 3026 11082 34646 13803 18011 35474 22733 3361734598 2430 11376 17648 19089 27031 33569 3748 31787 38672 1716 2854130394 18278 33786 34836 8313 26157 32033 2619 34491 37580 31387 3383435739 5034 11365 26172 24580 30460 33982 4375 14974 34935 6085 815925482 12728 23556 35511 2361 35221 35496 7948 15663 37449 12946 1302623162 9367 13954 16799 15553 18209 29641 9304 24815 26869 5095 2663930677 14012 20605 23633 12915 13984 30821 9349 16778 23849 16874 2654126754 15642 20257 28066 7505 14992 20745 547 5328 26296 5178 8851 26552

TABLE 8j Address of Parity Bit Accumulators (Rate ⅓) 7127 12217 1490317792 19690 23709 26904 31847 32174 37971 39934 43192 631 3892 3961 71109168 14664 20881 33763 34077 38290 38589 40587 1561 4952 12735 1705017363 23114 23432 26431 30725 34201 38679 41775 3120 6362 9346 1020219293 21581 26158 28110 28791 30854 37723 39609 937 3213 3271 8272 903515349 18735 23617 27626 33046 35819 42715 42 5281 15192 15731 2068723236 29529 31564 32442 35605 36703 42323 3415 5078 7595 8830 1629816735 18395 18860 20659 21190 24417 39339 1247 3506 4592 7574 1179914188 22214 27862 31190 33446 39010 39447 659 6732 8711 10845 1496720932 21392 24561 27950 30282 34491 39662 1574 6084 6401 10616 1549621480 22587 24801 28997 34755 40468 40765 1816 5243 8287 9380 1279513208 22838 23280 31453 35837 36957 38620 2526 5720 11010 12022 1520019448 27202 27673 29334 32919 36071 42350 542 3767 8589 14736 1759918679 20408 29296 37332 38338 40657 42203 1274 6050 11401 13088 1427117551 31621 32620 36895 37191 39291 43194 312 4625 6259 6839 10672 1669521781 27493 27928 31056 33505 41398 167 1811 6813 10155 10651 1554416043 23824 28470 32607 35112 37845 2477 2675 8067 19670 22707 2706929018 30917 33456 37625 40865 42750 2232 8590 13476 14000 16942 2302623964 26975 29689 33460 36770 41758 2199 4775 7747 8795 17270 1886621982 24102 29704 34123 34954 41148 2130 4709 11954 12300 19938 2529925579 28797 30414 36228 36617 42694 1336 22318 25169 18630 24904 2607119828 24680 29215 33916 41065 41539 14761 30074 40827 10013 20112 2593214530 21735 41427 12985 26680 37635 7003 9909 14113 16556 18312 2060618051 19132 21794 4506 10959 16641 13543 16372 29889 9717 22665 3732430086 36117 40152 19395 33829 38170 3120 17782 40104 1599 30981 352935514 10349 25365 5646 10000 25213 5839 12560 41786 20495 31791 347104251 31730 33042 1029 12241 28921 4009 32368 35306 7216 13773 3649512623 22397 34316 20441 24199 41893 15962 17883 25624 13355 13717 3566724883 27266 28103 24291 28357 34576 964 35256 39973 11315 18036 391202832 16014 25615 3789 7400 11418 9383 32137 37908 11721 30386 39012 796326523 43088 7442 11584 26585

TABLE 8k Address of Parity Bit Accumulators (Rate ¼) 4154 7271 1860826981 29145 30753 34895 36931 37422 42768 47366 47722 3011 5069 61569587 12589 20148 33306 36809 37089 44032 45205 48468 39 1332 8129 1965021273 25443 26292 28737 31676 33999 34500 38260 2180 2761 8052 1075016919 18907 23210 24269 26621 34815 39889 43751 1473 1960 13924 2141023195 27618 32955 36079 38702 41888 44387 44654 4943 6550 9829 1489315444 19815 24320 29734 33955 36141 42602 45015 1132 3914 6903 1215412305 16298 20487 25855 29304 32150 39228 47188 880 8771 13199 1596521881 22783 25410 28163 31814 34217 38887 40142 2890 7245 11208 1876121093 26680 31955 38349 40180 43274 43710 46286 296 571 2760 9305 1352914589 17815 28360 30693 33015 35716 39781 3678 9475 12627 13894 1626719135 22641 24756 28788 33357 35290 46414 2066 9907 11657 15142 1551621000 22945 27012 29663 40795 44925 47884 713 4869 6526 10360 1492021797 31226 35575 41795 42905 45382 45984 1015 4061 6411 8415 1149413574 23760 24879 27137 37539 42259 45488 8455 11853 14155 16832 1931819778 27886 28893 36425 41079 43947 48266 5393 17152 43557 17300 2504448036 25767 28037 31468 4322 42152 44324 27676 46770 47870 23456 2479130363 7899 10123 45744 7716 12923 33714 18718 30285 40475 1794 1803532276 26277 33598 38109 8757 21965 40705 7007 12090 17815 17010 2201037440 3493 13085 32557 10988 18098 20180 2166 11137 23546 15518 2055035071 26272 41471 46610 4430 14274 35788 23839 29219 43155 17336 2077032566 10570 16186 35139 5836 22534 38783 5863 36391 41378 5580 3097141722 5558 30075 39521 14465 39539 40407 3369 30151 46801 9211 3788046862

FIG. 2B illustrates a block diagram of a Bose Chaudhuri Hocquenghem(BCH) encoder 209, utilized with an LDPC encoder 203 and an interleaver211, according to exemplary embodiments of the present invention. Underthis scenario, the codes generated by the LDPC encoder 203 and the BCHencoder 209, can have a concatenated outer BCH code. Further, the outputof the LDPC encoder can be bit interleaved using the interleaver 211. Inone exemplary embodiment, the interleaver 211 can be a blockinterleaver. Alternatively, the interleaver 211 can be an optionalelement in the transmitter and instead an interleaver in a receiver(such as receiver 116) can be used to interleave decoder input.Additionally, a cyclic redundancy check (CRC) encoder (not shown) can beconnected to the BCH encoder 209 such that error detection can beachieved using cyclic redundancy check (CRC) codes. In one embodiment,the outer BCH code can be a 12 bit error correcting, withn_(bch)=k_(bch)+192, noting that n_(bch)=k_(ldpc).

By way of example, the BCH coding parameters are specified in thefollowing table (Table 9a):

TABLE 9a Coding Parameters (normal FEC Frame − LDPC Coded Block n_(ldpc)= 64800) BCH BCH Coded Block N_(bch) BCH t-Error LDPC Code Uncoded LDPCUncoded Block Correction Rate Block K_(bch) k_(ldpc) (bits) ¼ 1600816200 12 ⅓ 21408 21600 12 ⅖ 25728 25920 12 ½ 32208 32400 12 ⅗ 3668838880 12 ⅔ 43040 43200 10 ¾ 48408 48600 12 ⅘ 51648 51840 12 ⅚ 5384054000 10 8/9 57472 57600 8   9/10 58192 58320 8

By way of further example, the generator polynomial of the t errorcorrecting BCH encoder 209 is obtained by multiplying the first tpolynomials specified in the following table (Table 9b):

TABLE 9b BCH Polynomials (normal FEC Frame − LDPC Coded Block n_(ldpc) =64800) g₁(x) 1 + x² + x³ + x⁵ + x¹⁶ g₂(x) 1 + x + x⁴ + x⁵ + x⁶ + x⁸ +x¹⁶ g₃(x) 1 + x² + x³ + x⁴ + x⁵ + x⁷ + x⁸ + x⁹ + x¹⁰ + x¹¹ + x¹⁶ g₄(x)1 + x² + x⁴ + x⁶ + x⁹ + x¹¹ + x¹² + x¹⁴ + x¹⁶ g₅(x) 1 + x + x² + x³ +x⁵ + x⁸ + x⁹ + x¹⁰ + x¹¹ + x¹² + x¹⁶ g₆(x) 1 + x² + x⁴ + x⁵ + x⁷ + x⁸ +x⁹ + x¹⁰ + x¹² + x¹³ + x¹⁴ + x¹⁵ + x¹⁶ g₇(x) 1 + x² + x⁵ + x⁶ + x⁸ +x⁹ + x¹⁰ + x¹¹ + x¹³ + x¹⁵ + x¹⁶ g₈(x) 1 + x + x² + x⁵ + x⁶ + x⁸ + x⁹ +x¹² + x¹³ + x¹⁴ + x¹⁶ g₉(x) 1 + x⁵ + x⁷ + x⁹ + x¹⁰ + x¹¹ + x¹⁶ g₁₀(x)1 + x + x² + x⁵ + x⁷ + x⁸ + x¹⁰ + x¹² + x¹³ + x¹⁴ + x¹⁶ g₁₁(x) 1 + x² +x³ + x⁵ + x⁹ + x¹¹ + x¹² + x¹³ + x¹⁶ g₁₂(x) 1 + x + x⁵ + x⁶ + x⁷ + x⁹ +x¹¹ + x¹² + x¹⁶

The BCH encoding of information bits m=(m_(k) _(bch) ⁻¹, m_(k) _(bch)⁻², . . . m₁, m₀) into a codeword c=(m_(k) _(bch) ⁻¹, m_(k) _(bch) ⁻², .. . m₁, m₀, d_(n) _(bch) _(−k) _(bch) ⁻¹, d_(n) _(bch) _(−k) _(bch) ⁻²,. . . d₁, d₀) is achieved as follows: (1) multiply the messagepolynomial m(x)=(m_(k) _(bch) ⁻¹x^(k) ^(bch−1) +m_(k) _(bch) ⁻²x^(k)^(bch−1) + . . . +m₁x+m₀) by x^(n) ^(bch) ^(−k) ^(bch) ; (2) dividex^(n) ^(bch) ^(−k) ^(bch) (x) by the generator polynomial g(x), whered(x)=(d_(n) _(bch) _(−k) _(bch) ⁻¹x^(n) ^(bch) ^(−k) ^(bch) ⁻¹+ . . .+d₁x+d₀) is the remainder; and (3) set the codeword polynomialc(x)=x^(n) ^(bch) ^(−k) ^(bch) m+d(x).

In accordance with further exemplary embodiments, for 8-PSK, 16-APSK and32-APSK modulation formats, for example, the output of the LDPC encoder203 can be bit interleaved using the interleaver 211. Data is seriallywritten into the interleaver 211 column-wise (from top to bottom), andserially read out row-wise (from left to right, except for the rate 3/58-PSK case, where data is read out from right to left). Theconfiguration of the block interleaver 211 for each modulation format isillustrated in Table 10.

TABLE 10 Modulation Rows (n_(ldpc) = 64800) Rows (n_(ldpc) = 16200)Columns  8-PSK 21600 5400 3 16-APSK 16200 4050 4 32-APSK 12960 3240 5

FIG. 2D illustrates a flow chart of a process for performing encoding,interleaving and modulating source information bits, according toexemplary embodiments of the present invention. At step 231 theinformation bits are received and LDPC codes are generated at step 233.It is noted that the structure of the LDPC codes (stemming from thedesign of the parity check matrix) permits an efficient decodingprocess, whereby parallel computation engines can be utilized. Accordingto certain embodiment, the LDPC code can be generated without BCH codesand codes also can contain a CRC code. At step 235, the coded bits arealtered by the interleaver 211, as described above. Next the codes aremodulated per step 237 and are transmitted on the communication channel.

FIG. 3A illustrates a block diagram of a receiver, and FIG. 3Billustrates a flow chart depicting a process for decoding an encodedsignal, according to exemplary embodiments of the present invention. Atthe receiving side, a receiver 300 includes an antenna 301 that receivesthe waveforms emitted over the channel 114, which is depicted by step331 where the receiver 300 receives the transmitted signal. The receiverprovides a demodulator 303 that demodulates the received signal (Step333). By way of example, the signal may reflect a source signal receivedat the receiver 200, encoded and modulated based on the exemplaryencoding and modulation schemes described herein, and transmitted overthe channel 114. After demodulation, the received signals are forwardedto a decoder 305 for decoding the demodulated signal (Step 335). Thedecoder attempts to reconstruct the original source messages bygenerating messages, X′, in conjunction with a bit metric generator 307.According to certain embodiments, the decoder 305 can employ M parallelengines 309 to efficiently decode the received signals. By way ofexample, according to this parallel approach, M may correspond to thegroupings of M bit nodes for processing. In one exemplary embodiment,the demodulator 303 in accordance with the bit metric generator 307 canprovide a priori probabilities of log likelihood ratios of coded bits.It is contemplated that the above transmitter 200 and receiver 300 canbe deployed within a single wireless terminal, in which case a commonantenna system can be shared. The wireless terminal can for example beconfigured to operate within a satellite communication, a cellularsystem, wireless local area network (WLAN), etc. The LDPC codes,according to exemplary embodiments, can be used to variety of digitalvideo applications, such as MPEG (Motion Pictures Expert Group) packettransmission.

To appreciate the advantages offered by the present embodiments, it isinstructive to examine how LDPC codes are generated, as discussed inFIG. 4. FIG. 4 illustrates a sparse parity check matrix, according to anexemplary embodiment of the present invention. LDPC codes are long,linear block codes with sparse parity check matrix H_((n-k)xn).Typically the block length n ranges from thousands to tens of thousandsof bits. For example, a parity check matrix for an LDPC code of lengthn=8 and rate 1/2 is shown in FIG. 4. FIG. 5 illustrates a bipartitegraph of an LDPC code of the matrix of FIG. 4, according to an exemplaryembodiment of the present invention. Parity check equations imply thatfor each check node, the sum (over Galois Field (GF) 2) of all adjacentbit nodes is equal to zero. As seen in the figure, bit nodes occupy theleft side of the graph and are associated with one or more check nodes,according to a predetermined relationship. For example, corresponding tocheck node m₁, the following expression exists n₁+n₄+n₅+n₈=0 withrespect to the bit nodes.

Returning to the receiver 300, the LDPC decoder 305 is considered amessage passing decoder, whereby the decoder 305 aims to find the valuesof bit nodes. To accomplish this task, bit nodes and check nodesiteratively communicate with each other. The nature of thiscommunication is described below. From check nodes to bit nodes, eachcheck node provides to an adjacent bit node an estimate (“opinion”)regarding the value of that bit node based on the information comingfrom other adjacent bit nodes. For instance, in the above example if thesum of n₄, n₅ and n₈ “looks like” 0 to m₁, then m₁ would indicate to n₁that the value of n₁ is believed to be 0 (since n₁+n₄+n₅+n₈=0);otherwise m₁ would indicate to n₁ that the value of n₁ is believed tobe 1. Additionally, for soft decision decoding, a reliability measure isadded. From bit nodes to check nodes, each bit node relays to anadjacent check node an estimate about its own value based on thefeedback coming from its other adjacent check nodes. In the aboveexample n₁ has only two adjacent check nodes m₁ and m₃. If the feedbackcoming from m₃ to n₁ indicates that the value of n₁ is probably 0, thenn₁ would notify m₁ that an estimate of the value of n₁ is 0. For thecase in which the bit node has more than two adjacent check nodes, thebit node performs a majority vote (soft decision) on the feedback comingfrom its other adjacent check nodes before reporting that decision tothe check node it communicates. The above process is repeated until allbit nodes are considered to be correct (i.e., all parity check equationsare satisfied) or until a predetermined maximum number of iterations isreached, whereby a decoding failure is declared.

FIG. 6 is a diagram of a sub-matrix of a sparse parity check matrix,wherein the sub-matrix contains parity check values restricted to thelower triangular region, according to an exemplary embodiment. Asdescribed previously, the encoder 203 (of FIG. 2) can employ a simpleencoding technique by restricting the values of the lower triangulararea of the parity check matrix. According to an exemplary embodiment,the restriction imposed on the parity check matrix is of the form:H _((n−k)xn) =[A _((n−k)xk) B _((n−k)x(n−k))], where B is the lowertriangular.

Any information block i=(i₀, i₁, . . . , i_(k-1)) can be encoded to acodeword c=(i₀, i₁, . . . , i_(k-1), p₀, p₁, . . . , p_(n−k−1)) usingHc^(T)=0, and recursively solving for parity bits, for example:a ₀₀ i ₀ +a ₀₁ i ₁ + . . . +a _(0,k−1) i _(k-1) +p ₀=0

Solve p ₀a ₁₀ i ₀ +a ₁₁ i ₁ + . . . +a _(1,k−1) i _(k-1) +b ₁₀ p ₁=0

Solve p ₁and similarly for p ₂ ,p ₃ , . . . ,p _(1−k−1).

FIGS. 7A-7E illustrate modulation signal constellations, according toexemplary embodiments of the present invention.

FIG. 7A illustrates a QPSK constellation, including the associated bitlabeling, in accordance with an exemplary embodiment. In the context ofQPSK, bits 2 i, 2 i+1 Determine the i^(th) QPSK symbol, where i=0, 1, 2,. . . , (N/2)−1 and N is the coded LDPC block size. Alternatively, thebit positioning for the signal constellation of FIG. 7A can be expressedas specified below in Table 11 a (where ε_(x) represents average energyper symbol):

TABLE 11a Bit Label [x, y] Coordinates 00 [{square root over (ε_(x))} *cos(π/4.0), {square root over (ε_(x))} * sin(π/4.0)] 01 [{square rootover (ε_(x))} * cos(7.0 * π/4.0), {square root over (ε_(x))} * sin(7.0 *π/4.0)] 10 [{square root over (ε_(x))} * cos(3.0 * π/4.0), {square rootover (ε_(x))} * sin(3.0 * π/4.0)] 11 [{square root over (ε_(x))} *cos(5.0 * π/4.0), {square root over (ε_(x))} * sin(5.0 * π/4.0)]

FIG. 7B illustrates an 8-PSK constellation, including the associated bitlabeling, in accordance with an exemplary embodiment. In the context of8-PSK, bits 3 i, 3 i+1, 3 i+2 of the interleaver output determine thei^(th) 8-PSK symbol where i=0, 1, 2, . . . , (N/3)−1 and N is the codedLDPC block size—except rate 3/5, where bits 3 i+2, 3 i+1, 3 i of theinterleaver output determine the i^(th) 8-PSK symbol. Alternatively, thebit positioning for the signal constellation of FIG. 7B can be expressedas specified below in Table 11b (where ε_(x) represents average energyper symbol):

TABLE 11b Bit Label [x, y] Coordinates 000 [{square root over (ε_(x))} *cos(π/8.0), {square root over (ε_(x))} * sin(π/8.0)] 001 [{square rootover (ε_(x))} * cos(15.0 * π/8.0), {square root over (ε_(x))} *sin(15.0 * π/8.0)] 010 [{square root over (ε_(x))} * cos(7.0 * π/8.0),{square root over (ε_(x))} * sin(7.0 * π/8.0)] 011 [{square root over(ε_(x))} * cos(9.0 * π/8.0), {square root over (ε_(x))} * sin(9.0 *π/8.0)] 100 [{square root over (ε_(x))} * cos(3.0 * π/8.0), {square rootover (ε_(x))} * sin(3.0 * π/8.0)] 101 [{square root over (ε_(x))} *cos(13.0 * π/8.0), {square root over (ε_(x))} * sin(13.0 * π/8.0)] 110[{square root over (ε_(x))} * cos(5.0 * π/8.0), {square root over(ε_(x))} * sin(5.0 * π/8.0)] 111 [{square root over (ε_(x))} *cos(11.0 * π/8.0), {square root over (ε_(x))} * sin(11.0 * π/8.0)]

FIG. 7C illustrates a 16-APSK (4+12) constellation, including theassociated bit labeling, in accordance with an exemplary embodiment. Inthe context of 16-APSK, bits 4 i, 4 i+1, 4 i+2, 4 i+3 of the interleaveroutput determine the i^(th) 16-APSK symbol, where i=0, 1, 2, . . . ,(N/4)−1 and N is the coded LDPC block size. Alternatively, the bitpositioning for the signal constellation of FIG. 7C can be expressed asspecified below in Table 11c (where ε_(x) represents average energy persymbol, 4*R1²+12*R2²=16, and R1 represents the radius of the inner-mostring and R2 represents the radius of the outer ring):

TABLE 11c Bit Label [x, y] Coordinates 0000 [R2 * {square root over(ε_(x))} * cos(3.0 * π/12.0), R2 * {square root over (ε_(x))} *sin(3.0 * π/12.0)] 0001 [R2 * {square root over (ε_(x))} * cos(21.0 *π/12.0), R2 * {square root over (ε_(x))} * sin(21 * π/12.0)] 0010 [R2 *{square root over (ε_(x))} * cos(9.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(9 * π/12.0)] 0011 [R2 * {square root over (ε_(x))} *cos(15.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(15 * π/12.0)]0100 [R2 * {square root over (ε_(x))} * cos(π/12.0), R2 * {square rootover (ε_(x))} * sin(π/12.0)] 0101 [R2 * {square root over (ε_(x))} *cos(23.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(23 * π/12.0)]0110 [R2 * {square root over (ε_(x))} * cos(11.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(11 * π/12.0)] 0111 [R2 * {square root over(ε_(x))} * cos(13.0 * π/12.0), R2 * {square root over (ε_(x))} *sin(13 * π/12.0)] 1000 [R2 * {square root over (ε_(x))} * cos(5.0 *π/12.0), R2 * {square root over (ε_(x))} * sin(5 * π/12.0)] 1001 [R2 *{square root over (ε_(x))} * cos(19.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(19 * π/12.0)] 1010 [R2 * {square root over (ε_(x))} *cos(7.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(7 * π/12.0)]1011 [R2 * {square root over (ε_(x))} * cos(17.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(17 * π/12.0)] 1100 [R1 * {square root over(ε_(x))} * cos(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)]1101 [R1 * {square root over (ε_(x))} * cos(7.0 * π/4.0), R1 * {squareroot over (ε_(x))} * sin(7.0 * π/4.0)] 1110 [R1 * {square root over(ε_(x))} * cos(3.0 * π/4.0), R1 * {square root over (ε_(x))} * sin(3.0 *π/4.0)] 1111 [R1 * {square root over (ε_(x))} * cos(5.0 * π/4.0), R1 *{square root over (ε_(x))} * sin(5.0 * π/4.0)]

FIG. 7D illustrates a 32-APSK (4+12+16) constellation, including theassociated bit labeling, in accordance with an exemplary embodiment. Inthe context of 32-APSK (single belief decoding mode), bits 5 i, 5 i+1, 5i+2, 5 i+3, 5 i+4 of the interleaver output determine the i^(th) 32-APSKsymbol, where i=0, 1, 2, . . . , (N/5)−1 and N is the coded LDPC blocksize. Alternatively, the bit positioning for the signal constellation ofFIG. 7D can be expressed as specified below in Table 11d (where ε_(x)represents average energy per symbol, 4*R1²+12*R2²+16*R3²=32, and R1represents the radius of the inner-most ring, R2 represents the radiusof the middle ring and R3 represents the radius of the outer ring):

TABLE 11d Bit Label [x, y] Coordinates 00000 [R2 * {square root over(ε_(x))} * sin(π/4.0), R2 * {square root over (ε_(x))} * sin(π/4.0)]00001 [R2 * {square root over (ε_(x))} * sin(π/12.0), R2 * {square rootover (ε_(x))} * sin(5.0 * π/12.0)] 00010 [R2 * {square root over(ε_(x))} * sin(π/4.0), −R2 * {square root over (ε_(x))} * sin(π/4.0)]00011 [R2 * {square root over (ε_(x))} * sin(π/12.0), −R2 * {square rootover (ε_(x))} * sin(5.0 * π/12.0)] 00100 [−R2 * {square root over(ε_(x))} * sin(π/4.0), R2 * {square root over (ε_(x))} * sin(π/4.0)]00101 [−R2 * {square root over (ε_(x))} * sin(π/12.0), R2 * {square rootover (ε_(x))} * sin(5.0 * π/12.0)] 00110 [−R2 * {square root over(ε_(x))} * sin(π/4.0), −R2 * {square root over (ε_(x))} * sin(π/4.0)]00111 [−R2 * {square root over (ε_(x))} * sin(π/12.0), −R2 * {squareroot over (ε_(x))} * sin(5.0 * π/12.0)] 01000 [R3 * {square root over(ε_(x))} * cos(π/8.0), R3 * {square root over (ε_(x))} * sin(π/8.0)]01001 [R3 * {square root over (ε_(x))} * sin(π/8.0), R3 * {square rootover (ε_(x))} * cos(π/8.0)] 01010 [R3 * {square root over (ε_(x))} *sin(π/4.0), −R3 * {square root over (ε_(x))} * sin(π/4.0)] 01011 [0,−R3 * {square root over (ε_(x))}] 01100 [−R3 * {square root over(ε_(x))} * sin(π/4.0), R3 * {square root over (ε_(x))} * sin(π/4.0)]01101 [0, R3 * {square root over (ε_(x))}] 01110 [−R3 * {square rootover (ε_(x))} * cos(π/8.0), −R3 * {square root over (ε_(x))} *sin(π/8.0)] 01111 [−R3 * {square root over (ε_(x))} * sin(π/8.0), −R3 *{square root over (ε_(x))} * cos(π/8.0)] 10000 [R2 * {square root over(ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over (ε_(x))} *sin(π/12.0)] 10001 [R1 * {square root over (ε_(x))} * sin(π/4.0), R1 *{square root over (ε_(x))} * sin(π/4.0)] 10010 [R2 * {square root over(ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over (ε_(x))} *sin(π/12.0)] 10011 [R1 * {square root over (ε_(x))} * sin(π/4.0), −R1 *{square root over (ε_(x))} * sin(π/4.0)] 10100 [−R2 * {square root over(ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over (ε_(x))} *sin(π/12.0)] 10101 [−R1 * {square root over (ε_(x))} * sin(π/4.0), R1 *{square root over (ε_(x))} * sin(π/4.0)] 10110 [−R2 * {square root over(ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over (ε_(x))} *sin(π/12.0)] 10111 [−R1 * {square root over (ε_(x))} * sin(π/4.0), −R1 *{square root over (ε_(x))} * sin(π/4.0)] 11000 [R3 * {square root over(ε_(x))}, 0] 11001 [R3 * {square root over (ε_(x))} * sin(π/4.0), R3 *{square root over (ε_(x))} * sin(π/4.0)] 11010 [R3 * {square root over(ε_(x))} * cos(π/8.0), −R3 * {square root over (ε_(x))} * sin(π/8.0)]11011 [R3 * {square root over (ε_(x))} * sin(π/8.0), −R3 * {square rootover (ε_(x))} * cos(π/8.0)] 11100 [−R3 * {square root over (ε_(x))} *cos(π/8.0), R3 * {square root over (ε_(x))} * sin(π/8.0)] 11101 [−R3 *{square root over (ε_(x))} * sin(π/8.0), R3 * {square root over(ε_(x))} * cos(π/8.0)] 11110 [−R3 * {square root over (ε_(x))}, 0] 11111[−R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)]

FIG. 7E illustrates a 32-APSK (4+12+16) constellation, including theassociated bit labeling, in accordance with an exemplary embodiment. Inthe context of 32-APSK (layered belief decoding mode): (1) for rate 3/4,bits 5 i+3, 5 i+4, 5 i+2, 5 i+1, 5 i of the interleaver output determinethe i^(th) 32-APSK symbol, where i=0, 1, 2, . . . , (N/5)−1 and N is thecoded LDPC block size; (2) for rate 4/5, bits 5 i+1, 5 i+4, 5 i+3, 5i+2, 5 i of the interleaver output determine the i^(th) 32-APSK symbol,where i=0, 1, 2, . . . , (N/5)−1 and N is the coded LDPC block size; (3)for rates 5/6 and 8/9, bits 5 i+1, 5 i, 5 i+2, 5 i+3, 5 i+4 of theinterleaver output determine the i^(th) 32-APSK symbol, where i=0, 1, 2,. . . , (N/5)−1 and N is the coded LDPC block size; (4) for rate 9/10,bits 5 i+2, 5 i+3, 5 i+4, 5 i+1, 5 i of the interleaver output determinethe i^(th) 32-APSK symbol, where i=0, 1, 2, . . . , (N/5)−1 and N is thecoded LDPC block size. Alternatively, the bit positioning for the signalconstellation of FIG. 7E can be expressed as specified below in Table11e (where ε_(x) represents average energy per symbol,4*R1²+12*R2²+16*R3²=32, and R1 represents the radius of the inner-mostring, R2 represents the radius of the middle ring and R3 represents theradius of the outer ring):

TABLE 11e Bit Label [x, y] Coordinates 00000 [−R3 * {square root over(ε_(x))} * sin(π/4.0), R3 * {square root over (ε_(x))} * sin(π/4.0)]00001 [−R3 * {square root over (ε_(x))} * sin(π/8.0), R3 * {square rootover (ε_(x))} * cos(π/8.0)] 00010 [R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 00011 [0, R3 *{square root over (ε_(x))}] 00100 [−R2 * {square root over (ε_(x))} *sin (π/4.0), R2 * {square root over (ε_(x))} * sin(π/4.0)] 00101 [−R2 *{square root over (ε_(x))} * sin(π/12.0), R2 * {square root over(ε_(x))} * sin(5.0 * π/12.0)] 00110 [R2 * {square root over (ε_(x))} *sin(π/4.0), R2 * {square root over (ε_(x))} * sin(π/4.0)] 00111 [R2 *{square root over (ε_(x))} * sin(π/12.0), R2 * {square root over(ε_(x))} * sin(5.0 * π/12.0)] 01000 [−R3 * {square root over (ε_(x))} *cos(π/8.0), R3 * {square root over (ε_(x))} * sin(π/8.0)] 01001 [−R3 *{square root over (ε_(x))}, 0] 01010 [R3 * {square root over (ε_(x))} *sin(π/4.0), R3 * {square root over (ε_(x))} * sin(π/4.0)] 01011 [R3 *{square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 01100 [−R2 * {square root over (ε_(x))} *sin(5.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(π/12.0)] 01101[−R1 * {square root over (ε_(x))} * sin(π/4.0), R1 * {square root over(ε_(x))} * sin(π/4.0)] 01110 [R2 * {square root over (ε_(x))} *sin(5.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(π/12.0)] 01111[R1 * {square root over (ε_(x))} * sin(π/4.0), R1 * {square root over(ε_(x))} * sin(π/4.0)] 10000 [−R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 10001 [0,−R3 * {square root over (ε_(x))}] 10010 [R3 * {square root over(ε_(x))} * sin(π/4.0), −R3 * {square root over (ε_(x))} * sin(π/4.0)]10011 [R3 * {square root over (ε_(x))} * sin(π/8.0), −R3 * {square rootover (ε_(x))} * cos(π/8.0)] 10100 [−R2 * {square root over (ε_(x))} *sin(π/4.0), −R2 * {square root over (ε_(x))} * sin(π/4.0)] 10101 [−R2 *{square root over (ε_(x))} * sin(π/12.0), −R2 * {square root over(ε_(x))} * sin(5.0 * π/12.0)] 10110 [R2 * {square root over (ε_(x))} *sin(π/4.0), −R2 * {square root over (ε_(x))} * sin(π/4.0)] 10111 [R2 *{square root over (ε_(x))} * sin(π/12.0), −R2 * {square root over(ε_(x))} * sin(5.0 * π/12.0)] 11000 [−R3 * {square root over (ε_(x))} *sin(π/4.0), −R3 * {square root over (ε_(x))} * sin(π/4.0)] 11001 [−R3 *{square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 11010 [R3 * {square root over (ε_(x))} *cos(π/8.0), −R3 * {square root over (ε_(x))} * sin(π/8.0)] 11011 [R3 *{square root over (ε_(x))}, 0] 11100 [−R2 * {square root over (ε_(x))} *sin(5.0 * π/12.0), −R2 * {square root over (ε_(x))} * sin(π/12.0)] 11101[−R1 * {square root over (ε_(x))} * sin(π/4.0), −R1 * {square root over(ε_(x))} * sin(π/4.0)] 11110 [R2 * {square root over (ε_(x))} *sin(5.0 * π/12.0), −R2 * {square root over (ε_(x))} * sin(π/12.0)] 11111[R1 * {square root over (ε_(x))} * sin(π/4.0), −R1 * {square root over(ε_(x))} * sin(π/4.0)]

FIG. 8 illustrates a block diagram of a chip set that can be utilized inimplementing exemplary embodiments of the present invention. Withreference to FIG. 8, chip set 800 includes, for instance, processor andmemory components described with respect to FIG. 5 incorporated in oneor more physical packages. By way of example, a physical packageincludes an arrangement of one or more materials, components, and/orwires on a structural assembly (e.g., a baseboard) to provide one ormore characteristics such as physical strength, conservation of size,and/or limitation of electrical interaction.

In one embodiment, the chip set 800 includes a communication mechanismsuch as a bus 801 for passing information among the components of thechip set. A processor 803 has connectivity to the bus 801 to executeinstructions and process information stored in, for example, a memory805. The processor 803 includes one or more processing cores with eachcore configured to perform independently. A multi-core processor enablesmultiprocessing within a single physical package. Examples of amulti-core processor include two, four, eight, or greater numbers ofprocessing cores. Alternatively or in addition, the processor 503includes one or more microprocessors configured in tandem via the bus801 to enable independent execution of instructions, pipelining, andmultithreading. The processor 803 may also be accompanied with one ormore specialized components to perform certain processing functions andtasks such as one or more digital signal processors (DSP) 807, and/orone or more application-specific integrated circuits (ASIC) 1309. A DSP807 typically is configured to process real-world signals (e.g., sound)in real time independently of the processor 803. Similarly, an ASIC 1309can be configured to performed specialized functions not easilyperformed by a general purposed processor. Other specialized componentsto aid in performing the inventive functions described herein includeone or more field programmable gate arrays (FPGA) (not shown), one ormore controllers (not shown), or one or more other special-purposecomputer chips.

The processor 803 and accompanying components have connectivity to thememory 805 via the bus 801. The memory 805 may comprise various forms ofcomputer-readable media, e.g., including both dynamic memory (e.g., RAM)and static memory (e.g., ROM) for storing executable instructions that,when executed by the processor 803 and/or the DSP 807 and/or the ASIC1309, perform the process of exemplary embodiments as described herein.The memory 805 also stores the data associated with or generated by theexecution of the process.

The term “computer-readable medium” or “computer-readable media,” asused herein, refers to any medium that participates in providinginstructions for execution by the processor 803, and/or one or more ofthe specialized components, such as the one or more digital signalprocessors (DSP) 807, and/or one or more application-specific integratedcircuits (ASIC) 809. Such a medium may take many forms, including butnot limited to non-volatile media, volatile media, and transmissionmedia. Non-volatile media include, for example, read only memory (ROM),included within memory 805. Volatile media, for example, may includedynamic random access memory (RAM), included within memory 805.Transmission media may include copper or other conductive wiring, fiberoptics, or other physical transmission media, including the wires and/oroptical fiber that comprise bus 801. Transmission media can also takethe form of wireless data signals, such as those generated during radiofrequency (RF) and infrared (IR) data communications. Common forms ofcomputer-readable media include, for example, magnetic storage media(e.g., magnetic hard disks or any other magnetic storage medium), solidstate or semiconductor storage media (e.g., RAM, PROM, EPROM, FLASHEPROM, a data storage device that uses integrated circuit assemblies asmemory to store data persistently, or any other storage memory chip ormodule), optical storage media (e.g., CD ROM, CDRW, DVD, or any otheroptical storage medium), a or any other medium for storing data fromwhich a computer or processor can read.

Various forms of computer-readable media may be involved in providinginstructions to a processor for execution. For example, the instructionsfor carrying out at least part of the present invention may initially beborne on a magnetic disk of a remote computer. In such a scenario, theremote computer loads the instructions into main memory and sends theinstructions over a telephone line using a modem. A modem of a localcomputer system receives the data on the telephone line and uses aninfrared transmitter to convert the data to an infrared signal andtransmit the infrared signal to a portable computing device, such as apersonal digital assistance (PDA) and a laptop. An infrared detector onthe portable computing device receives the information and instructionsborne by the infrared signal and places the data on a bus. The busconveys the data to main memory, from which a processor retrieves andexecutes the instructions. The instructions received by main memory mayoptionally be stored on storage device either before or after executionby processor.

Moreover, as will be appreciated, a module or component (as referred toherein) may be composed of software component(s), which are stored in amemory or other computer-readable storage medium, and executed by one ormore processors or CPUs of the respective devices. As will also beappreciated, however, a module may alternatively be composed of hardwarecomponent(s) or firmware component(s), or a combination of hardware,firmware and/or software components. Further, with respect to thevarious exemplary embodiments described herein, while certain of thefunctions are described as being performed by certain components ormodules (or combinations thereof), such descriptions are provided asexamples and are thus not intended to be limiting. Accordingly, any suchfunctions may be envisioned as being performed by other components ormodules (or combinations thereof), without departing from the spirit andgeneral scope of the present invention.

FIG. 9 illustrates a block diagram of a computer system that can beutilized in implementing exemplary embodiments of the present invention.The computer system 900 includes a bus 901 or other communicationsmechanism for communicating information, and a processor 903 coupled tothe bus 901 for processing information. The processor may comprise oneor more of various types of general processors, and/or one or morespecialized components (not shown), such as the one or more digitalsignal processors (DSPs) and/or one or more application-specificintegrated circuits (ASICs). The computer system 900 also includes mainmemory 905, such as a random access memory (RAM) or other dynamicstorage device, coupled to the bus 901 for storing information andinstructions to be executed by the processor 903. Memory 905 can also beused for storing temporary variables or other intermediate informationduring execution of instructions to be executed by the processor 903.The computer system 900 further includes a read only memory (ROM) 907 orother static storage device coupled to the bus 901 for storing staticinformation and instructions for the processor 903. A storage device909, such as a magnetic disk or optical disk, is additionally coupled tothe bus 901 for storing information and instructions.

The computer system 900 can be coupled via the bus 901 to a display 911,such as a cathode ray tube (CRT), liquid crystal display, active matrixdisplay, or plasma display, for displaying information to a computeruser. An input device 913, such as a keyboard including alphanumeric andother keys, is coupled to the bus 901 for communicating information andcommand selections to the processor 903. Another type of user inputdevice is cursor control 915, such as a mouse, a trackball, or cursordirection keys for communicating direction information and commandselections to the processor 903 and for controlling cursor movement onthe display 911.

According to aspects of exemplary embodiments of the invention, dynamicand flexible architectures, apparatus and methods for implementing loadbalancing for traffic loads for multiple priorities, in accordance withexemplary embodiments, are provided by the computer system 900 inresponse to the processor 903 executing an arrangement of instructionscontained in main memory 905. Such instructions can be read into mainmemory 905 from another computer-readable medium, such as the storagedevice 909. Execution of the arrangement of instructions contained inmain memory 905 causes the processor 903 to perform the process stepsdescribed herein. One or more processors in a multi-processingarrangement can also be employed to execute the instructions containedin main memory 905. In alternative embodiments, hard-wired circuitry canbe used in place of or in combination with software instructions toimplement embodiments and aspects of the invention. Thus, embodiments ofthe present invention are not limited to any specific combination ofhardware circuitry and software.

The computer system 900 also includes a communications interface 917coupled to bus 901. The communications interface 917 provides a two-waydata communications, such as coupling to a network link 919 connected toa local network 921 or to or from remote terminals or controllers ofcommunications systems. For example, the communications interface 917can be a digital subscriber line (DSL) card or modem, an integratedservices digital network (ISDN) card, a cable modem, or a telephonemodem to provide a data communications connection to a correspondingtype of telephone line. As another example, communications interface 917can be a local area network (LAN) card (e.g., for Ethernet or anAsynchronous Transfer Model (ATM) network) to provide a datacommunications connection to a compatible LAN. Wireless links, such asfor satellite communications systems, can also be implemented. In anysuch implementation, communications interface 917 sends and receiveselectrical, electromagnetic, or optical signals that carry digital datastreams representing various types of information. Further, thecommunications interface 917 can include peripheral interface devices,such as a Universal Serial Bus (USB) interface, a PCMCIA (PersonalComputer Memory Card International Association) interface, etc.

The network link 919 typically provides data communications through oneor more networks to other data devices. For example, the network link919 can provide a connection through local network 921 to a hostcomputer 923, which has connectivity to a network 925 (e.g., a wide areanetwork (WAN) or the global packet data communications network nowcommonly referred to as the “Internet”) or to data equipment operated byservice provider. The local network 921 and network 925 both useelectrical, electromagnetic, or optical signals to convey informationand instructions. The signals through the various networks and thesignals on network link 919 and through communications interface 917,which communicate digital data with computer system 900, are exemplaryforms of carrier waves bearing the information and instructions.

The computer system 900 can send messages and receive data, includingprogram code, through the network(s), network link 919, andcommunications interface 917. In the Internet example, a server (notshown) can transmit requested code belonging to an application programfor implementing an embodiment of the present invention through thenetwork 925, local network 921 and communications interface 917. Theprocessor 903 can execute the transmitted code while being receivedand/or store the code in storage device 909, or other non-volatilestorage for later execution. In this manner, computer system 900 canobtain application code in the form of a carrier wave.

While exemplary embodiments of the present invention may provide forvarious implementations (e.g., including hardware, firmware and/orsoftware components), and, unless stated otherwise, all functions areperformed by a CPU or a processor executing computer executable programcode stored in a non-transitory memory or computer-readable storagemedium, the various components can be implemented in differentconfigurations of hardware, firmware, software, and/or a combinationthereof. Except as otherwise disclosed herein, the various componentsshown in outline or in block form in the figures are individually wellknown and their internal construction and operation are not criticaleither to the making or using of this invention or to a description ofthe best mode thereof.

In the preceding specification, various embodiments have been describedwith reference to the accompanying drawings. It will, however, beevident that various modifications may be made thereto, and additionalembodiments may be implemented, without departing from the broader scopeof the invention as set forth in the claims that follow. Thespecification and drawings are accordingly to be regarded in anillustrative rather than restrictive sense.

What is claimed is:
 1. A method comprising: accessing, by a processor ofa device, stored information representing a predetermined structuredparity check matrix of a Low Density Parity Check (LDPC) code, whereinthe stored information reflects a tabular format of rows and columns,wherein each row represents occurrences of one values within arespective column of the parity check matrix, and wherein the columns ofthe parity check matrix are derived according to a predeterminedoperation based on the respective rows of the stored tabularinformation; and encoding one or more blocks of information bits of asource signal based on the LDPC code to generate an LDPC encoded signal;wherein the LDPC encoding of the blocks of information bits (each blockbeing of a size of k_(ldpc) information bits, and each resulting encodedblock being of a size of n_(ldpc) code bits including parity bits p_(i),i=0, 1, 2, . . . , n_(ldpc)−k_(ldpc)−1), comprises: initializing paritybit accumulators a₀=a₁= . . . =a_(n) _(ldpc) _(−k) _(ldpc) ⁻¹=0; for aone of the blocks of information bits, divided into j sequential groups(each of a size of M information bits), and for j=1, 2, 3, . . .k_(ldpc)/M: (1) accumulating a first information bit of a j^(th) groupin certain of the parity bit accumulators reflected by accumulatoraddresses based on a j^(th) row of the stored tabular information; and(2) accumulating the remaining (M−1) information bits of the j^(th)group in certain of the parity bit accumulators reflected by accumulatoraddresses according to {x+m mod M*q} mod(n_(ldpc)−k_(ldpc)), wherein xdenotes an address of the parity bit accumulator corresponding to thefirst bit of the group, and q=(n_(ldpc)−k_(ldpc))/M; and after all ofthe information bits of the one block are accumulated, sequentiallyperforming operations (with respect to the parity bit accumulators)according to a_(i)=a_(i)⊕a_(i-1), i=1, 2, . . . (n_(ldpc)−k_(ldpc)−1),where the additions are in Galois Field (GF) 2; and wherein the paritybits p_(i), i=0, 1, . . . (n_(ldpc)−k_(ldpc)−1) are respectivelyreflected by the resulting parity bit accumulators a_(i), i=0, 1, . . .(n_(ldpc)−k_(ldpc)−1); and wherein the stored information representingthe structured parity check matrix comprises a one of the followingTables 1a through 1r, TABLE 1a Address of Parity Bit Accumulators (Rate9/10 - Coded Block Size 720) 10 62 53 15 54 56 5 3 8 34 23 45 10 60 2327 6 70 51 65 26 38 23 67 18 22 25 1 12 28 5 61 36 44 7 49 20 46 29 69 622 31 46 37 51 54 18 65 32 11 17 46 32 15 0 3 45 44 24 63 64 45 23

TABLE 1b Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 960) 88 70 81 43 6 64 29 13 18 82 1 35 10 6 47 53 38 22 57 1 78 687 15 78 48 73 37 26 82 13 17 52 62 19 29 58 14 79 27 86 16 19 2 7 95 4430 5 42 81 13 22 66 17 8 93 19 82 50 41 16 93 57

TABLE 1c Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 1440) 132 109 122 67 12 97 46 19 120 129 70 31 28 125 2 55 108 81134 59 136 49 30 139 40 69 38 123 100 141 46 75 64 109 134 47 120 29 2667 112 37 10 55 136 53 122 103 80 17 34 115 40 61 46 71 132 81 18 7 12113 6 143 108 113 122 11 108 69 110 63 124 141 2 115 100 133 18 15 133 051 106 40 115 101 62 67 136 17 50 80 10 75 37 126 19 40 25 122 40 129143 12 66 83 17 7 74 52 17 23 8 21 94 117 119 80 70 104 25 66 43 73 8898 111

TABLE 1d Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 2160) 36 153 142 127 136 157 182 151 108 197 106 63 108 49 182 35 889 134 43 56 105 30 175 104 181 66 115 96 5 78 211 52 57 194 119 128 972 23 196 37 2 171 184 177 10 15 56 17 2 43 84 121 142 35 8 21 62 107 184193 46 7 160 205 42 107 120 181 122 103 196 153 46 163 72 105 202 11 3186 157 176 186 129 0 27 201 140 154 191 155 6 105 124 118 55 44 197 8760 189 206 121 8 215 206 93 43 136 94 65 28 178 51 110 59 144 149 98 12149 107 184 61 122 99

TABLE 1e Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 2880) 92 133 95 39 78 91 251 284 262 92 89 204 15 226 74 150 73 3928 47 258 175 57 160 171 286 97 12 208 69 108 59 164 4 171 217 50 245171 139 18 122 35 97 30 26 160 53 81 72 286 20 236 259 66 105 11 0 146 7196 95 168 194 1 129 64 29 241 177 250 47 151 53 184 192 59 52 21 84 24887 264 280 103 278 137 154 175 56 273 192 43 80 183 95 134 245 142 33229 18 196 200 186 188 251 33 43 33 250 74 6 55 77 261 282 139 286 227135 163 89 252 151 250 138 286 205 32 137 4 44 87 137 192 158 189 138 50173 236 15 94 82 285 281 133 249 191 114 1 128 96 193 76 1 242 153 284156 53 42 92 160 113 247 81 196 275 103 168 117 262 116 166 137 177 8125 115 9 6 199 219 18 208 138 73 14 154 101

TABLE 1f Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 3600) 212 271 274 5 122 345 127 59 138 71 189 157 60 256 26 143 234105 190 224 240 217 129 58 135 2 349 221 227 336 171 194 358 169 77 33034 235 174 269 74 261 28 235 126 50 345 130 302 42 31 15 214 47 79 33989 180 178 9 38 192 89 49 332 256 222 183 187 140 88 137 213 307 190 137225 258 289 233 188 336 85 93 98 352 333 17 324 62 244 149 108 19 242292 340 303 65 150 166 95 282 169 278 61 113 234 122 207 52 107 37 296135 178 330 271 200 339 176 243 203 284 202 249 210 350 9 61 126 16 253317 108 91 298 287 160 237 31 72 247 124 38 347 169 113 346 24 266 21108 188 267 269 298 117 275 332 216 163 317 130 146 272 82 193 30 129 77282 7 327 292 319 5 99 276 305 125 169 303 80 225 60 92 304 7 36 86 46

TABLE 1g Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 4320) 273 190 207 371 331 258 135 416 306 12 291 293 262 215 396 7414 193 91 207 384 341 260 81 128 365 170 9 336 396 413 238 16 407 130 442 323 54 85 6 103 349 176 216 286 426 277 425 416 419 322 289 164 379189 1 292 319 363 345 132 134 423 366 146 381 235 88 111 206 4 121 426307 254 203 244 406 216 7 275 53 76 329 418 416 84 233 293 351 368 153410 101 183 196 400 170 65 192 357 31 43 46 245 428 304 51 1 144 351 319321 413 298 350 213 244 210 387 166 367 228 297 178 83 238 97 428 266165 197 423 115 265 43 104 172 122 144 227 407 65 166 210 73 311 94 351154 357 64 172 30 13 320 243 412 318 392 346 252 286 13 207 208 277 17867 161 394 351 45 17 295 196 251 326 356 145 168 411 262 54 51 177 398148 355 330 168 399 161 312 50 419 65 327 61 374 232 28 69 303 298 116221 52 270 165 103 398 283 243 184 364 348 7 209 362 221 187 343 184 190265 306 277 56 25 34 325 345 60 198 344 113 68 41 171 253 56 188 431 27256 106 421 22 274 279 67 298 294 79

TABLE 1h Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 5760) 35 247 105 399 280 268 513 68 161 104 460 466 156 253 305 39372 489 178 202 398 199 151 383 92 527 54 224 200 409 42 147 459 569 553312 242 180 155 10 216 458 361 318 104 489 206 52 22 56 123 538 264 295130 29 263 28 274 239 276 124 449 21 360 482 519 253 225 202 212 312 268338 558 200 43 291 436 27 84 231 40 521 95 142 558 361 475 462 319 41984 74 522 573 451 188 526 263 226 159 440 491 415 434 60 215 553 250 72209 18 436 311 210 327 524 536 18 15 211 11 453 22 452 289 305 351 187343 240 98 33 493 147 100 176 188 384 379 347 349 332 532 518 483 445496 203 269 304 459 344 311 574 128 429 538 527 479 125 43 508 228 315416 231 417 558 501 190 498 526 341 505 270 381 517 260 12 481 91 44 540104 339 295 172 467 569 121 137 474 221 567 444 506 104 526 327 547 134519 522 262 547 37 375 377 455 400 327 325 213 390 6 167 11 363 160 541337 185 61 225 7 233 450 407 323 288 38 463 95 274 279 377 423 411 227558 156 114 497 471 22 73 296 508 393 182 304 239 183 415 322 332 28 500106 470 358 505 461 302 342 68 255 90 416 368 487 177 531 161 84 314 391310 392 367 177 19 102 130 366 25

TABLE 1i Address of Parity Bit Accumulators (Rate ⅔ - Coded Block Size1080) 78 323 226 335 169 288 12 213 328 321 122 163 12 37 310 223 344 97346 195 180 325 22 311 56 121 26 187 148 109 302 119 332 251 289 166 19724 303 313 258 228 239 181 232 154 323 182 6 282 77 162 3 199 295 112251 33 50 61 139 208 95 228 121 216 356 302 349 201 324 14

TABLE 1j Address of Parity Bit Accumulators (Rate ⅘ - Coded Block Size1080) 90 67 188 117 28 125 186 1 146 99 22 197 60 85 44 147 118 41 42133 8 75 142 17 30 97 158 93 46 71 30 109 182 195 16 143 60 10 105 33166 185 142 85 168 86 133 159 104 137 91 24 110 167 31 36 46 142 186 6389 139 116 99 5 88 176 195 193 12 44 185 168 37 146 141 166 101 66 37200 45 136 89 90 19 152 111 94 179 84 211 26 183 64 113 60 1 80 129 190179 6 121 20 159 88 131

TABLE 1k Address of Parity Bit Accumulators (Rate 8/9 - Coded Block Size720) 34 78 37 17 72 76 43 35 2 4 79 37 40 60 51 17 4 70 59 49 50 22 6331 46 20 69 73 40 70 57 55 38 22 43 46 40 71 14 17 61 26 21 45 4 36 1 6026 33 46 55 21 36 27 13

TABLE 1l Address of Parity Bit Accumulators (Rate 8/9 - Coded Block Size1080) 20 77 70 31 96 45 86 3 24 65 34 3 0 21 74 67 28 5 106 71 16 41 1895 72 17 6 59 40 69 22 71 64 101 86 83 96 85 46 119 96 37 70 99 0 89 4659 80 65 74 63 44 57 102 79 76 5 54 115 8 109 74 119 32 105 118 48 57 6244 89 30 80 97 114 60 65 115 40 5 111 52 9 27 108 105 79 116 38 47 32 3879 36 34 51 56 94 119 49 114 119 21 78 51 1 22 87 37 66 15

TABLE 1m Address of Parity Bit Accumulators (Rate 8/9 - Coded Block Size1440) 68 49 138 87 16 89 62 39 140 1 106 75 12 141 46 67 100 9 26 87 1241 94 83 128 73 106 35 20 113 10 55 16 81 122 135 136 97 38 111 140 77102 143 60 105 86 71 88 61 130 39 136 121 134 75 92 145 98 151 12 5 50 764 125 94 152 9 6 56 9 130 96 93 114 60 93 103 48 157 139 132 157 115 7261 79 64 14 31 80 130 95 140 46 131 92 74 139 5 122 75 145 14 19 121 22143 121 86 119

TABLE 1n Address of Parity Bit Accumulators (Rate 8/9 - Coded Block Size2160) 116 121 22 107 120 113 90 115 168 225 70 199 208 137 190 99 220113 34 207 52 177 94 235 204 229 66 171 100 85 218 123 16 113 2 23 96 7326 159 120 169 138 199 104 65 130 139 96 161 194 143 104 209 226 39 236125 182 79 140 13 50 79 28 193 118 188 89 34 224 61 50 128 81 46 156 9111 156 37 175 72 105 239 64 137 131 176 182 135 148 18 95 100 54 215224 174 103 165 238 87 145 214 207 89 182 55 53 38 159

TABLE 1o Address of Parity Bit Accumulators (Rate 8/9 - Coded Block Size2880) 33 174 30 142 266 282 240 78 291 229 80 43 156 132 134 303 50 31287 239 68 186 92 75 59 203 255 37 171 139 287 45 101 23 89 52 20 271 38109 84 32 111 225 183 314 101 110 142 163 44 25 206 302 173 5 86 272 1839 237 199 140 86 248 159 56 167 215 283 76 254 190 187 148 291 310 5753 99 90 134 151 199 111 30 227 148 51 167 33 294 190 147 173 84 175 10835 317 138 111 300 73 306 292 224 106 307 274 202 153 79 58 195 131 10249 242 51 9 28 275 6 287 54 246 313 106 88 49 315 42 218 265 212 239 85306 147

TABLE 1p Address of Parity Bit Accumulators (Rate 8/9 - Coded Block Size3600) 267 282 5 84 96 78 167 18 276 240 117 303 136 175 169 324 117 73360 4 379 398 265 253 146 11 62 89 114 227 342 31 26 284 295 49 239 137124 350 118 266 191 155 213 310 20 73 384 231 396 323 216 317 150 129232 58 27 245 272 18 59 253 62 376 44 337 293 392 42 396 87 270 91 25284 2 22 157 8 169 355 174 71 330 336 156 11 325 343 265 226 395 101 263163 60 152 303 250 245 206 289 382 354 57 368 212 201 271 214 120 237 1168 362 174 180 269 315 7 233 112 290 11 157 183 351 284 9 95 240 233 335261 152 78 267 348 253 42 75 78 75 29 98 64 84 385 378 54 39 152 132 29841 3 396 171 183 397 328 47 336 197 218 214 19 266 57 166 285 265 284214 75 5 239 74 46 244 313 317 127 8 3 65 50 60 177 310 119 325 136 36134 152 154 59 103 323 245 369 120 148 328 387 21 20 355 13 238 384 193154 351 121 322 390 44 66 326 39

TABLE 1q Address of Parity Bit Accumulators (Rate 8/9 - Coded Block Size4320) 30 196 79 344 162 460 169 79 210 252 30 83 389 334 100 47 199 11210 305 344 333 474 454 400 137 475 29 328 137 67 453 228 258 371 16 8268 197 38 174 403 56 41 25 52 309 303 239 152 81 379 106 452 443 31 474149 238 119 465 314 349 366 406 458 395 152 229 38 432 457 421 360 113247 244 144 178 315 189 97 212 62 375 166 356 397 2 307 79 436 385 314411 287 159 389 392 190 77 115 316 118 50 284 59 53 329 67 277 42 177466 331 380 144 335 402 52 48 449 126 151 160 273 70 143 53 440 436 321262 469 271 379 374 55 394 181 279 57 168 176 225 134 322 267 220 418203 308 270 332 257 398 82 379 104 167 117 141 82 168 119 332 470 370165 96 361 51 463 225 363 460 468 151 461 103 444 357 359 357 203 188 1350 379 385 256 274 393 123 408 434 142 96 426 414 343 22 106 277 434108 363 110 257 407 85 353 204 45 307 424 39 230 376 41 346 416 259 124

TABLE 1r Address of Parity Bit Accumulators (Rate 8/9 - Coded Block Size5760) 353 507 64 261 477 315 226 338 72 128 203 524 180 202 549 634 189460 321 307 339 402 117 164 461 342 193 78 145 236 119 63 100 365 496418 210 341 285 136 376 482 304 510 468 31 274 75 587 550 182 409 30 365461 19 184 599 351 66 28 627 2 475 143 352 175 161 163 637 166 159 33138 486 307 580 583 384 8 573 524 380 465 510 366 451 154 93 258 525 304358 286 434 410 458 26 442 565 530 385 548 99 207 142 119 321 177 529372 111 213 517 492 276 71 473 407 479 325 351 298 62 219 368 361 476 56304 558 543 554 515 527 621 379 447 56 482 560 469 205 637 453 334 18500 469 244 395 102 230 593 92 547 160 491 103 266 541 50 233 156 77 72397 39 464 305 68 284 519 307 35 281 349 44 191 275 460 296 232 348 543332 626 40 23 28 31 205 512 476 107 519 60 458 224 9 406 148 341 346 442270 544 283 259 571 503 363 157 472 425 170 107 384 425 288 467 86 199323 564 536 513 10 167 352 500 48 104 432 347 311 392 118 571 396 145584 609 328 145 50 403 181 625 159 73 169 271 265 626 552 327 564 439132 55 384 221 57 75 477 292 598 16 273 148 90 209 266 160 451 98 20
 143274.


2. A method according to claim 1, wherein row indices of 1's in a columnindex j*M (j=0, 1, 2, 3, . . . , k_(ldpc)/M−1) of the parity checkmatrix are given at the j^(th) row according to the one Table.
 3. Amethod according to claim 1, wherein the LDPC code is of a structurethat facilitates use of a plurality of parallel engines for decoding theencoded signal.
 4. A method according to claim 1, further comprising:modulating the LDPC encoded signal according to a signal constellationreflecting one of QPSK (Quadrature Phase Shift Keying), OQPSK (OffsetQPSK), PSK (Phase Shift Keying), 8-PSK, 16-APSK (Amplitude PSK), and32-APSK.
 5. A method according to claim 1, further comprising:modulating the LDPC encoded signal according to a signal constellationthat comprises a one of the following formats (where ε_(x) representsaverage energy per symbol), a QPSK (Quadrature Phase Shift Keying)constellation having bit labeling and x-y bit positioning according tothe following table: Bit Label [x, y] Coordinates 00 [{square root over(ε_(x))} * cos(π/4.0), {square root over (ε_(x))} * sin(π/4.0)] 01[{square root over (ε_(x))} * cos(7.0 * π/4.0), {square root over(ε_(x))} * sin(7.0 * π/4.0)] 10 [{square root over (ε_(x))} * cos(3.0 *π/4.0), {square root over (ε_(x))} * sin(3.0 * π/4.0)] 11 [{square rootover (ε_(x))} * cos(5.0 * π/4.0), {square root over (ε_(x))} * sin(5.0 *π/4.0)]

an 8-PSK (Phase Shift Keying) constellation having bit labeling and x-ybit positioning according to the following table: Bit Label [x, y]Coordinates 000 [{square root over (ε_(x))} * cos(π/8.0), {square rootover (ε_(x))} * sin(π/8.0)] 001 [{square root over (ε_(x))} * cos(15.0 *π/8.0), {square root over (ε_(x))} * sin(15.0 * π/8.0)] 010 [{squareroot over (ε_(x))} * cos(7.0 * π/8.0), {square root over (ε_(x))} *sin(7.0 * π/8.0)] 011 [{square root over (ε_(x))} * cos(9.0 * π/8.0),{square root over (ε_(x))} * sin(9.0 * π/8.0)] 100 [{square root over(ε_(x))} * cos(3.0 * π/8.0), {square root over (ε_(x))} * sin(3.0 *π/8.0)] 101 [{square root over (ε_(x))} * cos(13.0 * π/8.0), {squareroot over (ε_(x))} * sin(13.0 * π/8.0)] 110 [{square root over(ε_(x))} * cos(5.0 * π/8.0), {square root over (ε_(x))} * sin(5.0 *π/8.0)] 111 [{square root over (ε_(x))} * cos(11.0 * π/8.0), {squareroot over (ε_(x))} * sin(11.0 * π/8.0)]

a 16-APSK (Amplitude Phase Shift Keying) constellation, of a 4+12bit/ring format, having bit labeling and x-y bit positioning accordingto the following table (where R1 represents the radius of an inner ringand R2 represents the radius of an outer ring, and 4*R1²+12*R2²=16): BitLabel [x, y] Coordinates 0000 [R2 * {square root over (ε_(x))} *cos(3.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(3.0 * π/12.0)]0001 [R2 * {square root over (ε_(x))} * cos(21.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(21 * π/12.0)] 0010 [R2 * {square root over(ε_(x))} * cos(9.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(9 *π/12.0)] 0011 [R2 * {square root over (ε_(x))} * cos(15.0 * π/12.0),R2 * {square root over (ε_(x))} * sin(15 * π/12.0)] 0100 [R2 * {squareroot over (ε_(x))} * cos(π/12.0), R2 * {square root over (ε_(x))} *sin(π/12.0)] 0101 [R2 * {square root over (ε_(x))} * cos(23.0 * π/12.0),R2 * {square root over (ε_(x))} * sin(23 * π/12.0)] 0110 [R2 * {squareroot over (ε_(x))} * cos(11.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(11 * π/12.0)] 0111 [R2 * {square root over (ε_(x))} *cos(13.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(13 * π/12.0)]1000 [R2 * {square root over (ε_(x))} * cos(5.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(5 * π/12.0)] 1001 [R2 * {square root over(ε_(x))} * cos(19.0 * π/12.0), R2 * {square root over (ε_(x))} *sin(19 * π/12.0)] 1010 [R2 * {square root over (ε_(x))} * cos(7.0 *π/12.0), R2 * {square root over (ε_(x))} * sin(7 * π/12.0)] 1011 [R2 *{square root over (ε_(x))} * cos(17.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(17 * π/12.0)] 1100 [R1 * {square root over (ε_(x))} *cos(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 1101 [R1 *{square root over (ε_(x))} * cos(7.0 * π/4.0), R1 * {square root over(ε_(x))} * sin(7.0 * π/4.0)] 1110 [R1 * {square root over (ε_(x))} *cos(3.0 * π/4.0), R1 * {square root over (ε_(x))} * sin(3.0 * π/4.0)]1111 [R1 * {square root over (ε_(x))} * cos(5.0 * π/4.0), R1 * {squareroot over (ε_(x))} * sin(5.0 * π/4.0)]

a 32-APSK constellation, of a 4+12+16 bit/ring format, having a bitlabeling and x-y bit positioning according to the following table (whereR1 represents the radius of an inner ring, R2 represents the radius ofan middle ring and R3 represents the radius of an outer ring, and4*R1²+12*R2²=16*R3²=32): Bit Label [x, y] Coordinates 00000 [R2 *{square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00001 [R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00010[R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 00011 [R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00100[−R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00110[−R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 00111 [−R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 01000[R3 * {square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 01001 [R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 01010 [R3 *{square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 01011 [0, −R3 * {square root over (ε_(x))}] 01100[−R3 * {square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 01101 [0, R3 * {square root over (ε_(x))}] 01110[−R3 * {square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 01111 [−R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 10000 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 10001 [R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10010 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over(ε_(x))} * sin(π/12.0)] 10011 [R1 * {square root over (ε_(x))} *sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)] 10100 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 10101 [−R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10110 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over(ε_(x))} * sin(π/12.0)] 10111 [−R1 * {square root over (ε_(x))} *sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)] 11000 [R3 *{square root over (ε_(x))}, 0] 11001 [R3 * {square root over (ε_(x))} *sin(π/4.0), R3 * {square root over (ε_(x))} * sin(π/4.0)] 11010 [R3 *{square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 11011 [R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 11100 [−R3 *{square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 11101 [−R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 11110 [−R3 *{square root over (ε_(x))}, 0] 11111 [−R3 * {square root over (ε_(x))} *sin(π/4.0), −R3 * {square root over (ε_(x))} * sin(π/4.0)]

a 32-APSK constellation, of a 4+12+16 bit/ring format, having bitlabeling and x-y bit positioning according to the following table (whereR1 represents the radius of an inner ring, R2 represents the radius of amiddle ring and R3 represents the radius of an outer ring, and4*R1²+12*R2²+16*R3²=32): Bit Label [x, y] Coordinates 00000 [−R3 *{square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 00001 [−R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 00010 [R3 *{square root over (ε_(x))} * sin(π/8.0), R3 * {square root over(ε_(x))} * cos(π/8.0)] 00011 [0, R3 * {square root over (ε_(x))}] 00100[−R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00110[R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00111 [R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 01000[−R3 * {square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 01001 [−R3 * {square root over (ε_(x))}, 0] 01010[R3 * {square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 01011 [R3 * {square root over (ε_(x))} *cos(π/8.0), R3 * {square root over (ε_(x))} * sin(π/8.0)] 01100 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 01101 [−R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 01110 [R2 *{square root over (ε_(x))} * sin(5.0 π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 01111 [R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10000 [−R3 *{square root over (ε_(x))} * sin(π/8.0), −R3 * {square root over(ε_(x))} * cos(π/8.0)] 10001 [0, −R3 * {square root over (ε_(x))}] 10010[R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 10011 [R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 10100 [−R2 *{square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 10101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 10110[R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 10111 [R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 11000[−R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 11001 [−R3 * {square root over (ε_(x))} *cos(π/8.0), −R3 * {square root over (ε_(x))} * sin(π/8.0)] 11010 [R3 *{square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 11011 [R3 * {square root over (ε_(x))}, 0] 11100[−R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {squareroot over (ε_(x))} * sin(π/12.0)] 11101 [−R1 * {square root over(ε_(x))} * sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)]11110 [R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 *{square root over (ε_(x))} * sin(π/12.0)] 11111 [R1 * {square root over(ε_(x))} * sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)].


6. A method according to claim 1, further comprising: encoding, prior tothe LDPC encoding, the one or more blocks of information bits of thesource signal based on a t-error Bose Chaudhuri Hocquenghem (BCH) code.7. A method according to claim 6, further comprising: interleaving theLDPC encoded signal.
 8. A method according to claim 7, furthercomprising: modulating the interleaved signal according to a signalconstellation that comprises a one of the following formats (where ε_(x)represents average energy per symbol), a QPSK (Quadrature Phase ShiftKeying) constellation having bit labeling and x-y bit positioningaccording to the following table: Bit Label [x, y] Coordinates 00[{square root over (ε_(x) )} * cos(π/4.0), {square root over (ε_(x) )} *sin(π/4.0)] 01 [{square root over (ε_(x) )} * cos(7.0 * π/4.0), {squareroot over (ε_(x) )} * sin(7.0 * π/4.0)] 10 [{square root over (ε_(x))} * cos(3.0 * π/4.0), {square root over (ε_(x) )} * sin(3.0 * π/4.0)]11 [{square root over (ε_(x) )} * cos(5.0 * π/4.0), {square root over(ε_(x) )} * sin(5.0 * π/4.0)]

an 8-PSK (Phase Shift Keying) constellation having bit labeling and x-ybit positioning according to the following table: Bit Label [x, y]Coordinates 000 [{square root over (ε_(x))} * cos(π/8.0), {square rootover (ε_(x))} * sin(π/8.0)] 001 [{square root over (ε_(x))} * cos(15.0 *π/8.0), {square root over (ε_(x))} * sin(15.0 * π/8.0)] 010 [{squareroot over (ε_(x))} * cos(7.0 * π/8.0), {square root over (ε_(x))} *sin(7.0 * π/8.0)] 011 [{square root over (ε_(x))} * cos(9.0 * π/8.0),{square root over (ε_(x))} * sin(9.0 * π/8.0)] 100 [{square root over(ε_(x))} * cos(3.0 * π/8.0), {square root over (ε_(x))} * sin(3.0 *π/8.0)] 101 [{square root over (ε_(x))} * cos(13.0 * π/8.0), {squareroot over (ε_(x))} * sin(13.0 * π/8.0)] 110 [{square root over(ε_(x))} * cos(5.0 * π/8.0), {square root over (ε_(x))} * sin(5.0 *π/8.0)] 111 [{square root over (ε_(x))} * cos(11.0 * π/8.0), {squareroot over (ε_(x))} * sin(11.0 * π/8.0)]

a 16-APSK (Amplitude Phase Shift Keying) constellation, of a 4+12bit/ring format, having bit labeling and x-y bit positioning accordingto the following table (where R1 represents the radius of an inner ringand R2 represents the radius of an outer ring, and 4*R1²+12*R2²=16): BitLabel [x, y] Coordinates 0000 [R2 * {square root over (ε_(x))} *cos(3.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(3.0 * π/12.0)]0001 [R2 * {square root over (ε_(x))} * cos(21.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(21 * π/12.0)] 0010 [R2 * {square root over(ε_(x))} * cos(9.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(9 *π/12.0)] 0011 [R2 * {square root over (ε_(x))} * cos(15.0 * π/12.0),R2 * {square root over (ε_(x))} * sin(15 * π/12.0)] 0100 [R2 * {squareroot over (ε_(x))} * cos(π/12.0), R2 * {square root over (ε_(x))} *sin(π/12.0)] 0101 [R2 * {square root over (ε_(x))} * cos(23.0 * π/12.0),R2 * {square root over (ε_(x))} * sin(23 * π/12.0)] 0110 [R2 * {squareroot over (ε_(x))} * cos(11.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(11 * π/12.0)] 0111 [R2 * {square root over (ε_(x))} *cos(13.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(13 * π/12.0)]1000 [R2 * {square root over (ε_(x))} * cos(5.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(5 * π/12.0)] 1001 [R2 * {square root over(ε_(x))} * cos(19.0 * π/12.0), R2 * {square root over (ε_(x))} *sin(19 * π/12.0)] 1010 [R2 * {square root over (ε_(x))} * cos(7.0 *π/12.0), R2 * {square root over (ε_(x))} * sin(7 * π/12.0)] 1011 [R2 *{square root over (ε_(x))} * cos(17.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(17 * π/12.0)] 1100 [R1 * {square root over (ε_(x))} *cos(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 1101 [R1 *{square root over (ε_(x))} * cos(7.0 * π/4.0), R1 * {square root over(ε_(x))} * sin(7.0 * π/4.0)] 1110 [R1 * {square root over (ε_(x))} *cos(3.0 * π/4.0), R1 * {square root over (ε_(x))} * sin(3.0 * π/4.0)]1111 [R1 * {square root over (ε_(x))} * cos(5.0 * π/4.0), R1 * {squareroot over (ε_(x))} * sin(5.0 * π/4.0)]

a 32-APSK constellation, of a 4+12+16 bit/ring format, having bitlabeling and x-y bit positioning according to the following table (whereR1 represents the radius of an inner ring, R2 represents the radius of amiddle ring and R3 represents the radius of an outer ring, and4*R1²+12*R2²+16*R3²=32): Bit Label [x, y] Coordinates 00000 [R2 *{square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * Sin(π/4.0)] 00001 [R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00010[R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 00011 [R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00100[−R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00110[−R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 00111 [−R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 01000[R3 * {square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 01001 [R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 01010 [R3 *{square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 01011 [0, −R3 * {square root over (ε_(x))}] 01100[−R3 * {square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 01101 [0, R3 * {square root over (ε_(x))}] 01110[−R3 * {square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 01111 [−R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 10000 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 10001 [R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10010 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over(ε_(x))} * sin(π/12.0)] 10011 [R1 * {square root over (ε_(x))} *sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)] 10100 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 10101 [−R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10110 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over(ε_(x))} * sin(π/12.0)] 10111 [−R1 * {square root over (ε_(x))} *sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)] 11000 [R3 *{square root over (ε_(x))}, 0] 11001 [R3 * {square root over (ε_(x))} *sin(π/4.0), R3 * {square root over (ε_(x))} * sin(π/4.0)] 11010 [R3 *{square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 11011 [R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 11100 [−R3 *{square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 11101 [−R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 11110 [−R3 *{square root over (ε_(x))}, 0] 11111 [−R3 * {square root over (ε_(x))} *sin(π/4.0), −R3 * {square root over (ε_(x))} * sin(π/4.0)]

a 32-APSK constellation, of a 4+12+16 bit/ring format, having bitlabeling and x-y bit positioning according to the following table (whereR1 represents the radius of an inner ring, R2 represents the radius of amiddle ring and R3 represents the radius of an outer ring, and4*R1²+12*R2²+16*R3²=32): Bit Label [x, y] Coordinates 00000 [−R3 *{square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 00001 [−R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 00010 [R3 *{square root over (ε_(x))} * sin(π/8.0), R3 * {square root over(ε_(x))} * cos(π/8.0)] 00011 [0, R3 * {square root over (ε_(x))}] 00100[−R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00110[R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00111 [R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 01000[−R3 * {square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 01001 [−R3 * {square root over (ε_(x))}, 0] 01010[R3 * {square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 01011 [R3 * {square root over (ε_(x))} *cos(π/8.0), R3 * {square root over (ε_(x))} * sin(π/8.0)] 01100 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 01101 [−R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 01110 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 01111 [R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10000 [−R3 *{square root over (ε_(x))} * sin(π/8.0), −R3 * {square root over(ε_(x))} * cos(π/8.0)] 10001 [0, −R3 * {square root over (ε_(x))}] 10010[R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 10011 [R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 10100 [−R2 *{square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 10101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 10110[R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 10111 [R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 11000[−R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 11001 [−R3 * {square root over (ε_(x))} *cos(π/8.0), −R3 *{square root over (ε_(x))} * sin(π/8.0)] 11010 [R3 *{square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 11011 [R3 * {square root over (ε_(x))}, 0] 11100[−R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {squareroot over (ε_(x))} * sin(π/12.0)] 11101 [−R1 * {square root over(ε_(x))} * sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)]11110 [R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 *{square root over (ε_(x))} * sin(π/12.0)] 11111 [R1 * {square root over(ε_(x))} * sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)].


9. A method comprising: accessing, by a processor of a device, storedinformation representing a predetermined structured parity check matrixof a Low Density Parity Check (LDPC) code, wherein the storedinformation reflects a tabular format of rows and columns, wherein eachrow represents occurrences of one values within a respective column ofthe parity check matrix, and wherein the columns of the parity checkmatrix are derived according to a predetermined operation based on therespective rows of the stored tabular information; and encoding one ormore blocks of information bits of a source signal based on the LDPCcode to generate an LDPC encoded signal; wherein the LDPC encoding ofthe blocks of information bits (each block being of a size of k_(ldpc)information bits, and each resulting encoded block being of a size ofn_(ldpc) code bits including parity bits p_(i), i=0, 1, 2, . . . ,n_(ldpc)−k_(ldpc)−1), comprises: initializing parity bit accumulatorsa₀=a₁= . . . =a_(n) _(ldpc) _(−k) _(ldpc) ⁻¹=0; for a one of the blocksof information bits, divided into j sequential groups (each of a size ofM information bits), and for j=1, 2, 3, . . . k_(ldpc)/M: (1)accumulating a first information bit of a j^(th) group in certain of theparity bit accumulators reflected by accumulator addresses based on aj^(th) row of the stored tabular information; and (2) accumulating theremaining (M−1) information bits of the j^(th) group in certain of theparity bit accumulators reflected by accumulator addresses according to${\{ {x + {m\mspace{14mu}{mod}\mspace{14mu} M}} \} - {\{ {\frac{x + {m\mspace{14mu}{mod}\mspace{14mu} M}}{M} - \frac{x}{M}} \}*M}},$wherein the division within the second bracketed term reflects integerdivision, and x denotes an address of the parity bit accumulatorcorresponding to the first bit of the group; and after all of theinformation bits are accumulated, starting with M=1, sequentiallyperforming operations (with respect to the parity bit accumulators)according to the following (where the additions are in Galois Field (GF)2), $\begin{matrix}{a_{M} = {a_{M} \oplus p_{0}}} \\{a_{2M} = {a_{2M} \oplus a_{M}}} \\{a_{3M} = {a_{3M} \oplus a_{2M}}}\end{matrix}$ ⋮      ⋮     ⋮ $\begin{matrix}{a_{n_{ldpc} - k_{ldpc} - M} = {a_{n_{ldpc} - k_{ldpc} - M} \oplus}} & {a_{n_{ldpc} - k_{ldpc} - {2M}}\;}\end{matrix}$ ⋮          ⋮            ⋮a₁ = a₁ ⊕ a_(n_(ldpc) − k_(ldpc) − M) a_(M + 1) = a_(M + 1) ⊕ a₁a_(2M + 1) = a_(2M + 1) ⊕ a_(M + 1)    ⋮       ⋮      ⋮ $\begin{matrix}{a_{n_{ldpc} - k_{ldpc} - M + 1} = {a_{n_{ldpc} - k_{ldpc} - M + 1} \oplus}} & {a_{n_{ldpc} - k_{ldpc} - {2M} + 1}\;}\end{matrix}$ ⋮          ⋮            ⋮a₂ = a₂ ⊕ a_(n_(ldpc) − k_(ldpc) − M + 1) a_(M + 2) = a_(M + 2) ⊕ a₂a_(2M + 2) = a_(2M + 2) ⊕ a_(M + 2)    ⋮       ⋮      ⋮ $\begin{matrix}{a_{n_{ldpc} - k_{ldpc} - M + 2} = {a_{n_{ldpc} - k_{ldpc} - M + 2} \oplus}} & {a_{n_{ldpc} - k_{ldpc} - {2M} + 2}\;}\end{matrix}$ ⋮          ⋮            ⋮a₃ = a₃ ⊕ a_(n_(ldpc) − k_(ldpc) − M + 2) a_(M + 3) = a_(M + 3) ⊕ a₃a_(2M + 3) = a_(2M + 3) ⊕ a_(M + 3)    ⋮       ⋮      ⋮ $\begin{matrix}{a_{n_{ldpc} - k_{ldpc} - M + 3} = {a_{n_{ldpc} - k_{ldpc} - M + 3} \oplus}} & {a_{n_{ldpc} - k_{ldpc} - {2M} + 3}\;}\end{matrix}$ ⋮          ⋮            ⋮ $\begin{matrix}{a_{M - 1} = {a_{M - 1} \oplus a_{n_{ldpc} - k_{ldpc} - 2}}} \\{a_{{2M} - 1} = {a_{{2M} - 2} \oplus a_{M - 1}}} \\{a_{{3M} - 1} = {a_{{3M} - 1} \oplus a_{{2M} - 1}}}\end{matrix}$ ⋮      ⋮     ⋮ $\begin{matrix}{a_{n_{ldpc} - k_{ldpc} - 1} = {a_{n_{ldpc} - k_{ldpc} - 1} \oplus}} & {a_{n_{ldpc} - k_{ldpc} - M - 1}\;}\end{matrix}$ wherein the parity bits p_(i), i=0, 1, . . .(n_(ldpc)−k_(ldpc)−1) are respectively reflected by the resulting paritybit accumulators a_(i), i=0, 1, . . . (n_(ldpc)−k_(ldpc)−1); and whereinthe stored information representing the structured parity check matrixcomprises a one of the following Tables 9a through 9k, TABLE 9a Addressof Parity Bit Accumulators (Rate 9/10) 405 3342 3664 6278 121 538 45794801 776 3102 3279 5298 135 1119 4225 6307 440 902 3893 5464 139 32895101 5543 1016 1893 3076 5942 2253 2759 5611 6055 335 1122 3260 5610 4362337 2781 4648 2027 2451 5009 5137 1165 2440 4331 6125 1704 1858 39865327 938 2077 3080 5007 1239 1668 4309 4524 1464 2825 3640 4979 16823716 4081 5851 2709 2976 5931 6213 3811 5917 6342 1558 3818 4076 22905606 5807 2080 2467 4655 465 2866 4971 873 1881 4624 1301 2270 5161 16372567 4787 1380 4475 5563 258 2769 3845 240 1228 3387 46 5258 6393 5831652 4139 2983 4137 5095 601 3064 3299 1821 6025 6123 775 3243 5674 8223142 4768 3068 3255 6474 1006 2795 4896 2791 2997 5909 2583 3167 64271395 4398 5579 608 2248 3277 2491 5104 5580 2437 4228 4444 246 568 3849253 3723 4093 242 3968 6360 700 964 4904 1470 4714 5146 866 1382 38011107 3368 4559 1679 1981 6041 1868 5706 6063 1602 1894 5142 289 27264941 1943 3179 6347 2186 4446 5537 1055 3361 5448 531 2627 4448 14673414 5117 1738 4095 4628 1254 4214 5078 2218 5681 5936 272 5085 6284 1391218 6269 576 3127 4258 1122 3584 3844 1795 4712 6092 1071 3754 4913 7281868 3004 586 2425 2573 1986 3826 5894 217 1148 4123 1136 3201 3286 11384906 5344 548 3705 6148 2510 3974 4654 1846 2949 5959 2374 4890 60091495 2556 4359 582 4226 4406 233 3425 3922 1017 3734 5431 2358 5105 6251260 418 2567 1627 2737 5360 788 3492 5646 1561 2057 4812 2147 5844 6217952 2938 5458 1468 1837 4577 234 5186 6359 372 2505 2680 112 461 33111294 3488 6350 1377 2441 6280 841 2776 5751 295 2591 5086 1628 4822 50803920 5608 5788 641 3885 4916 1482 3689 5845 2930 3257 5936 750 4659 47331864 2899 4301 1068 1963 5753 2214 4295 4650 1367 3170 4306 1519 41075104 289 4410 4959 1252 5166 6162 389 1624 4422 1420 1543 4360 669 33213631 125 1396 3536 2955 5317 6367 561 2194 4127 2206 4179 6352 794 35495771 2570 3692 4924 2001 3095 4990 2380 5638 6039 733 2805 3687 27043062 6013 187 2154 5745 861 1833 5750 1197 2312 4677 941 2008 4171 9944565 5542 2058 3148 5976 789 1130 5079 448 4531 4763 1082 3375 5742 34555065 5744 621 1691 4313 90 4103 5953 1592 3266 3800 3144 5789 6418 2702561 3650 668 2477 6348 2011 3060 4880 1490 3886 4777 122 2583 6348 24842643 5308 714 3867 4171 192 2798 3938 2420 4733 6067 647 1656 3776 856080 6232 1058 3109 4875 3035 3305 5118 1711 4216 6044 918 2044 4085 4582522 4675 1113 2240 6268 1686 2087 5113 2385 2773 6280 1405 3216 57372016 4555 4733 853 3414 4395 3344 5214 5751 306 1153 5579

TABLE 9b Address of Parity Bit Accumulators (Rate 8/9) 185 1982 50906885 2051 2208 6645 7139 463 930 3108 5287 267 4014 6164 6820 1118 16293252 5478 1939 2411 4705 6527 3131 3252 5283 6315 1376 4003 5928 68751744 2522 4828 5888 775 1312 4686 6012 1147 2917 5313 5516 1657 28523653 6751 2580 3234 5634 5767 2344 2721 4417 6418 179 3305 3726 7140 2653322 4581 6309 443 2495 4394 4866 437 1796 3762 4139 768 1957 3793 3966647 892 4421 5589 990 2583 2887 4756 1066 1924 3116 6195 1993 3020 53755699 2781 4456 6173 6700 1280 1782 3254 5823 1102 1476 3325 5079 7171636 5021 5053 718 1445 2691 5432 1965 3073 5711 6010 1941 2496 48026018 2517 3299 5556 6486 825 3944 5793 6425 666 2499 2522 4531 287 6193347 3816 964 1328 4743 5169 1157 2369 4523 7043 127 4266 4568 6180 3073640 4260 6893 292 4052 6794 7117 3713 4114 6485 7015 916 1840 4808 5220139 438 3527 4645 654 1723 3612 4033 47 4410 4716 7198 1432 3782 41266347 41 1835 4267 5105 228 4313 5213 6963 894 3161 4884 5093 1561 28143746 6634 1393 1792 5407 5863 685 1078 2679 3088 1529 1937 5427 57811056 3146 4779 6602 649 2204 2568 6951 2768 3151 5521 6676 2074 24845833 6967 2398 3331 4515 5561 1280 3728 5934 6182 2485 3373 6190 68151141 3276 4393 6389 104 3339 7107 656 3450 5083 1912 3649 7037 273 21196733 916 4161 4570 2206 4605 6266 2610 3601 5771 723 1363 3961 2300 27906200 4199 4441 6771 1495 2820 5471 936 1329 5098 1475 5488 6486 11853676 4992 2330 5321 6307 2004 2901 5853 3133 3465 5656 120 4787 5879 3841757 4790 701 2989 6954 193 3359 3727 1352 3685 4958 1982 2227 5529 18413055 6728 225 498 6919 2731 4716 6809 1503 2052 5524 1234 3886 5007 13414384 7124 434 868 6365 2928 5292 5711 2569 4525 7013 2659 3072 6131 541995 5083 202 4311 5089 2258 6221 6630 1715 4295 6096 2435 4296 4435 9003540 5913 1671 3425 5981 1627 2049 5389 1946 3883 4259 1194 3432 60181903 6028 7168 67 3683 6193 2604 3891 5706 216 4278 4516 908 2717 54972309 4658 6455 1338 4593 6133 2279 5039 6588 334 4056 5129 3244 54606040 685 5104 6933 1369 2978 5006 2318 4819 7028 639 809 3032 585 15472797 966 3231 6705 1573 3363 6546 2085 6713 7136 1171 3970 5141 249 27694607 1519 4336 4827 377 1688 5622 3204 4717 6716 576 1078 3713 4697 57657128 1933 5226 6382 708 1625 2782 3166 5564 6505 808 2529 5679 64 11073749 1971 3071 4053 2298 4369 6479 1255 3962 5119 2359 5902 6978 1693333 3750 739 3475 6479 2380 3302 6020 1153 2982 6933 108 3675 4989 16843397 4607 2468 3309 5749 1567 3494 5287 2695 5500 6779 1650 3987 5381952 3655 5634 931 4061 5859 1862 3208 5942 114 1175 4355 59 3906 64521337 4180 7050 1052 2851 5200 2014 3149 6787 662 2573 4810 2249 60256192 1868 2250 6544 702 5004 6942 488 4582 6161

TABLE 9c Address of Parity Bit Accumulators (Rate ⅚) 798 1195 3207 35565147 5412 7636 8021 181 3530 5203 5661 7617 8048 10135 10609 1462 18983635 3961 6209 6648 8552 9391 761 2127 2918 5450 7539 7636 9676 98091878 2332 5152 5494 7238 7765 9607 9727 181 3351 5105 5496 7409 77029598 10763 433 2788 3838 5588 5828 7800 8720 9731 488 2907 3472 63276569 8352 8930 10689 89 2842 5508 6026 7669 8121 10349 10699 1925 22314325 5010 6583 7643 8721 9846 1073 1231 3228 4187 5319 6420 7491 8521154 2531 4592 5601 7458 7695 10201 10581 479 881 2553 5231 5431 78478862 9787 391 818 3787 4243 5817 7830 8104 10055 97 588 2769 3729 59736278 8902 9993 2045 2185 4299 6169 6816 8287 8827 10767 507 1663 27293810 4901 5789 7930 9212 2496 2802 4651 5027 6717 7163 9596 10444 1592056 4328 4854 6630 8590 9452 10469 105 1425 3252 3895 5416 6726 92049691 518 2749 3784 4758 5853 6843 8190 10706 331 2785 4978 5396 71628264 9814 10120 418 2240 2800 4818 6481 7079 8751 10595 1066 2927 41305387 6921 8198 9866 10247 25 3567 3892 5833 6308 7967 8287 10482 54 6792617 4622 4734 6949 8644 9208 214 525 4266 4365 6258 6756 8899 9914 20302273 4200 4413 6808 6929 9081 10322 810 1196 3735 4282 6022 6390 88119881 869 3411 3871 5997 7129 8067 9328 10212 833 7114 8123 432 2458 41081764 7069 9592 4174 5900 7187 2292 5716 8280 2941 4153 5310 3285 39186052 794 3044 8493 1528 2043 4966 2117 9315 10277 1191 2175 6178 14695270 7449 1107 1504 6235 2293 4650 6746 839 4508 9493 1715 5088 89313454 4487 9120 2059 7336 9626 3162 4847 8433 3098 9173 9491 3195 631710336 1402 2396 7200 1190 4378 7312 3132 3499 10186 1505 1947 10088 13563312 9270 4853 7227 8577 1760 7218 9050 1124 1500 9030 1133 1501 84841277 2932 10769 369 6143 7263 2624 4740 8068 2270 5183 10587 1490 52785741 2996 5955 10051 2646 5143 7804 3515 5866 9203 2007 4063 7813 27846381 6663 1535 4845 8402 2345 6141 9480 7229 9659 10068 5821 8323 8658388 5608 7239 4440 5599 8039 3254 3863 10116 145 4960 9463 4161 65336951 854 7196 8816 4022 7710 10676 1111 2194 8266 627 3218 3319 18844623 8735 1904 6509 9830 898 1433 3632 788 3712 8292 1668 7197 9130 3304454 10156 244 9082 10160 2683 3844 4759 1266 1752 5956 781 5063 103341256 1626 4876 1758 7765 8001 980 3659 7851 4149 8190 10202 92 3468 5352825 5942 7041 3015 7100 10738 3478 5859 8168 3629 9571 9750 5503 68188354 3328 7496 10540 169 4810 9788 4408 5712 6625 1988 5507 9347 4615210 8677 263 4203 8549 4588 7551 9631 2122 2239 8785 6645 9519 106242312 4343 8735 2199 4041 7078 1817 7474 8339 2908 6305 9881 3070 907710184 1137 6336 9262 437 2562 7750 671 2647 6444 3094 5542 5834 24984042 7138 3933 8184 8378 769 2671 9268 425 3579 5432 4120 4369 8476 5463291 5723 2273 2530 7559 425 1494 5071 275 1890 9065 4492 5010 10023 1471404 5990 4047 9339 10134 5177 7388 9568 2151 7534 10210 191 2601 63671124 3094 9452 1405 7140 9375 3908 9782 10082 1902 4924 8442 1706 43236831 1786 3732 6867 7563 8939 10016 5784 8885 10703 6173 8155 10542 30114950 7607 3283 8830 10655 895 5348 8081 2444 6732 7821 750 6367 6530

TABLE 9d Address of Parity Bit Accumulators (Rate ⅘) 498 2356 3399 46315536 7415 9550 9825 11986 499 722 3381 4400 7825 8864 9980 10902 12000923 1278 3976 5353 6383 7233 9807 11841 12067 1027 1141 3080 3450 62706615 8936 10053 12197 241 641 2589 3938 5948 7939 8405 10918 12913 11401748 3891 3977 5929 6450 8852 11141 11465 389 720 2956 3508 5292 63907424 9013 11890 913 2029 3157 6116 6139 8615 9640 10504 12410 1169 23563348 5141 5417 8732 9775 10888 11893 2068 2926 4223 6046 7006 9224 965112316 12691 1872 2497 4581 6490 8352 8820 10713 10983 12827 883 13382907 3415 6435 7383 9426 9937 11822 2638 2906 5312 5413 8136 9226 1011712244 12602 223 2800 4527 5538 6773 9346 9604 11204 12275 277 2712 38925465 5996 7851 10705 11551 12726 2053 2383 4042 4524 6654 7155 9091 938111287 1645 2733 3773 4901 5829 8913 9297 11284 12363 596 1703 2826 46574790 7024 7407 10286 10768 1260 7640 10440 413 1758 7516 6709 6900 110711638 11242 12568 247 4966 8252 2125 3685 7002 252 10234 11279 17 19215116 2515 4974 7892 2470 8033 12635 8169 10285 10536 7131 7997 117311646 4100 6581 5489 8335 10367 4315 5206 7834 3661 8534 10114 4825 853711665 4735 7855 11729 3636 7050 12359 5855 11577 12216 3709 4041 119741302 4819 9598 3726 5951 12780 439 6839 12862 6107 6862 10014 329 34009601 4365 4963 6828 2659 10871 12147 2956 5165 12608 1292 3562 8246 16949213 10369 558 1639 7845 5331 8084 10216 4385 4729 6706 5253 5424 11744718 1662 8953 8672 9013 10984 3992 4522 9006 1971 3055 6477 6282 75429563 3542 10674 12427 2869 8558 8790 2382 7955 11422 2227 5687 109177260 10148 11466 866 2025 6459 807 8584 11291 3185 5589 8581 724 421310711 6951 7549 12599 2034 2386 10704 306 2866 11776 1115 7630 9974 2267681 10061 1262 8047 11342 2579 11466 11672 5616 5900 9675 214 525 101892502 4013 9398 4192 8827 11901 749 8020 11632 2689 10394 12856 45 333112206 1852 3988 10681 1080 8893 11333 2708 11688 12168 144 4672 102896772 7703 8784 562 733 7714 768 5510 9791 519 9482 10071 1462 5139 91181443 2000 4859 1636 3443 6279 2989 3370 5667 5155 6176 7256 2052 52617773 2950 8290 11050 5767 6931 7984 4358 6356 10596 2486 10860 129191421 3168 9846 5989 8551 10654 4504 4762 12565 4925 6522 10829 7308 850312839 2383 7034 7547 3957 9245 12567 3857 9346 12337 3692 6689 6950 30844828 7816 977 3692 6597 1538 7007 9577 623 8432 10784 6408 7355 10231946 9879 12496 7515 8521 10900 4040 8421 10792 3361 5178 6908 2236 873510552 3647 6779 9745 5516 6702 12914 272 11360 11827 1847 4653 12103 257344 9583 2454 11437 12443 2047 4203 6137 6285 10091 11506 3281 46569090 4289 8798 12488 1220 9341 10946 73 3759 7981 6859 8176 10167 17554703 5322 1434 10905 12144 2380 3454 8174 1259 11673 12041 408 485212932 3116 5666 7879 2986 8641 10037 1022 6055 11595 1604 5858 7579 18605406 12830 2547 5839 9415 454 2602 4342 2697 5238 9006

TABLE 9e Address of Parity Bit Accumulators (Rate ¾) 755 3136 3253 55418180 13010 14277 15226 464 989 2773 3063 5246 5711 7829 10703 687 21745068 6955 8933 9180 12238 12247 620 868 3613 7063 7491 9977 11659 122311121 3221 3985 7303 8598 9677 11994 15459 239 3514 3734 5618 7483 944313290 14309 624 1641 4395 4791 8232 8520 11653 13714 1764 3468 3630 68838179 10354 10666 12589 5441 6021 9211 10116 11365 12476 15587 16031 11913709 4945 5821 9932 13549 13712 15675 4312 4559 6892 9729 11121 1284714493 15725 2522 4963 7683 8080 10332 10545 13579 15279 2324 2660 465010336 12099 12402 14149 14535 6217 6529 9102 11077 11401 13051 1424716145 1900 4014 6973 9765 10139 13297 15029 15931 356 3856 4735 819710020 13408 13819 16041 589 3148 4079 5870 6141 9278 11221 11732 31625352 6442 7233 8287 11507 13756 15666 1600 8280 14758 8404 8921 132481796 8643 13329 3470 5959 10511 1771 2651 10918 5690 14326 14698 49697444 13930 3426 9264 13439 6079 7897 12750 731 5131 12199 4567 945315026 804 12393 12657 1363 2349 15827 2393 5056 11552 183 11487 15154 331989 15052 352 2157 14479 2459 2678 11725 7572 8993 11156 4590 1050110934 3970 6836 16007 6430 6525 9597 2015 12757 14985 1842 6677 769212934 14875 15425 1165 6320 9437 1205 6831 8927 3986 8773 15795 73108501 14143 5813 10378 10472 3293 12137 15600 750 6051 8898 7955 1359516006 947 6895 16179 1474 5536 11069 214 1979 5872 1373 1461 13091 811612210 15540 188 2677 6413 2785 6824 14251 2798 8431 12629 470 1655 38724471 6408 8522 8263 11449 16194 9329 9687 11535 21 6478 13326 2904 714111399 701 7076 11584 3166 5197 15397 5328 5731 7774 875 12344 15421 917713008 14984 3884 7246 14544 3334 6747 10089 4492 10028 13128 2463 1243114331 2429 11404 14714 4661 11689 15261 6515 12787 14813 3354 9539 98579146 12412 12863 585 4001 7578 2300 7776 13341 3839 4001 14733 7541 982715058 5177 10853 12062 4861 10697 11004 1976 4984 9453 1118 10773 139501800 2888 4942 5525 10278 13858 1141 8799 14032 5552 8722 11930 375510366 15563 3879 6873 9914 1236 10327 13474 10007 12774 15695 2178 904716151 6256 7420 11075 7780 12124 14020 5611 7207 15439 2529 4322 150872714 5217 9884 81 10799 11594 1845 7854 12328 2480 4360 8883 1107 699110377 3479 5761 14289 5639 8855 9053 1460 3703 11295 7710 12577 143754720 12673 14956 1176 12155 13882 2187 6857 12985 1622 5874 9437 9422765 14378 3492 5768 12701 6432 14722 14794 11046 13036 15948 2904 42117521 229 592 4897 1616 8035 11683 10569 13395 14431 4474 6712 1515813340 13920 15592 5030 13245 15131 1061 6169 6794 328 6771 12242 839810475 10827 535 5368 9184 1903 5121 11454 745 2003 14697 503 3281 114353200 8219 8491 8299 9504 11601 4128 8160 16124 2994 4032 9680

TABLE 9f Address of Parity Bit Accumulators (Rate ⅔) 1615 2039 820011116 12879 13266 14888 1056 2837 5958 7722 10531 13028 16131 321 41966772 8327 18370 21171 21440 2720 4996 7486 11437 15927 16234 21032 2504778 5126 9839 16614 18590 21299 36 10862 13201 15758 17702 20512 213104548 8263 11202 12249 14424 17146 20605 521 2272 5846 7080 11967 1564217973 1858 5497 5858 7892 13057 15657 19262 65 1964 3694 6305 7236 1292414509 648 3736 6461 10779 13755 17583 19163 4991 6081 9123 11807 1214418877 20967 667 1787 6412 8270 13080 15684 19871 7185 7366 14404 1701117561 19430 21050 2701 4406 9153 9479 15365 19423 21462 3942 7315 1093314239 17054 17558 19977 1427 5839 8022 10208 16873 16924 21529 60 64597405 9609 11824 16053 19264 1956 4737 6790 9007 12579 16313 19839 69498003 10138 12354 14675 17960 20107 3267 6813 10410 12761 14996 1515117838 975 1375 3246 6456 9683 9895 14572 496 4250 9354 10365 14249 1672419585 4187 5342 7802 10016 10840 13690 14811 954 9023 12299 15481 1730819923 20256 1554 2755 4407 4842 10638 16587 17877 1953 3616 8712 1220614211 16877 21233 1295 4174 4522 9604 12613 14892 17298 500 3106 533412580 12669 15443 18409 2283 8824 9896 13581 13889 20424 20765 1332116111 18888 6938 17206 19746 1784 4153 15066 9407 14334 18336 5350 694210093 3170 8370 11789 905 1308 8307 3052 5479 14093 1269 16063 194422686 4519 8777 1756 3659 11721 3002 11645 18023 8978 10622 20164 884611139 13721 3066 10762 13957 3464 11167 13550 16215 18615 18961 767615415 18065 5396 10017 18358 7850 16492 18269 3531 16286 18989 573911192 13524 1009 18408 18920 6625 13662 15264 3505 12215 20200 842612029 20522 8496 19529 20705 2218 6541 11495 2253 5667 20631 2320 573919782 2335 8137 9814 1688 9285 15288 1393 8162 12727 3355 11661 14163142 10231 20568 9158 12878 13257 14324 17954 19658 2483 4417 18250 66110219 14001 6896 10200 14537 8802 17982 20021 2787 9042 14255 3101 1318018975 1164 8420 16306 6500 9735 12804 11842 14862 19904 7598 8199 179104273 17028 20983 544 9997 17358 3136 19586 20591 1785 5171 9714 838814782 18328 32 6240 10995 865 5080 8797 624 11476 14648 2163 7348 13686101 3574 18935 7330 13508 14000 5743 7379 9514 1592 11437 17432 48936775 20933 762 2691 7070 3030 19170 20360 4299 7845 19138 1978 658912314 2757 11178 14780 4956 5881 21471 3392 7590 19773 15990 19435 202271888 5932 16298 4085 5882 12449 4813 16665 20934 5522 9375 18435 1046612470 16771 11805 16606 21277 856 5550 18431 1094 12130 15534 1454917123 19074 5076 13100 17343 10615 16455 20767 13544 15381 16991 382918367 21333 15456 15532 19920 6866 15766 18286 6461 8677 12234 202612038 20327 3839 8318 10649 4613 11022 15972 3757 13434 15910 4519 646111133

TABLE 9g Address of Parity Bit Accumulators (Rate ⅗) 487 2424 5103 629414728 16989 22394 22707 1634 5235 7897 8219 10473 10926 15226 17159 78368222 10026 12421 17812 20194 21551 25762 178 4183 5238 8916 11565 1351317234 23622 2619 3761 6539 10279 11943 16294 19745 22819 1097 3310 529710950 12939 13749 18284 19985 5062 8675 11402 13351 14655 16741 2055322461 5862 7897 12406 13503 16929 17631 20389 22142 1160 8004 9813 1354014666 18003 22246 24879 157 6179 13015 16673 17089 19482 23223 243241568 3396 5983 13072 13336 18349 18521 21010 3632 5935 7011 12522 1585717935 18950 23596 7555 8375 10646 12391 15071 20478 22501 23402 20002378 7387 11854 13513 21598 24971 25503 476 2578 7339 8402 13753 1614719513 22512 1646 7593 8714 9846 12535 14403 21897 22723 913 3205 53846134 13821 16335 23236 24236 502 1494 5665 8092 9094 13273 18152 238563571 5849 7970 10318 16538 19009 19186 24775 1768 5020 10749 15104 1844621191 21392 25505 279 7272 9982 10336 13151 15451 18316 22103 2005 40264677 7991 9235 13384 14754 23731 1319 3499 6567 7679 11063 15094 1526717449 6162 6797 10759 11683 12866 13911 17226 22718 2382 9187 1180816423 18162 19122 21873 22911 216 1114 7075 14485 16966 19607 2291424691 721 2693 6387 8821 17550 19330 22719 24673 972 2842 8828 993312899 15009 15268 23746 1947 4539 10078 12725 13876 18387 20589 247831755 4300 6903 8799 14179 14485 20595 24429 3854 4896 7018 10751 1401614346 16861 19163 3859 4085 5919 7733 15182 16468 19409 21431 1371 676310705 10999 14233 17684 21160 22018 2356 5185 5651 12200 12308 1638418868 21030 6600 8655 9801 11712 13854 16725 20795 25380 1692 3627 69627462 10218 21056 21314 24003 16314 19603 22678 1179 19957 21941 1416319047 24512 10474 20933 24258 461 8308 11535 7361 11441 12375 40 641710855 6001 22526 23757 1071 3964 9467 2756 6525 23536 449 3246 1178212053 19545 21812 2670 3701 10363 7809 17817 20062 2900 6138 24663 70429061 22324 7149 12133 15790 7464 15848 22261 4406 15275 21965 2305 824015658 844 3405 18366 1893 2451 17338 5810 17934 20992 2244 4845 2415817878 18964 23878 5429 22314 24712 303 14398 24478 15836 18743 218264587 17442 23891 9067 19984 25568 12659 20803 25727 5409 6673 23824 969215061 18694 861 1169 16870 12226 14993 20284 13054 14784 20185 160 1550123163 614 18992 23847 4719 15363 20481 19129 23171 24212 5465 2165025118 3669 15823 17361 12767 13112 21339 4658 14270 17975 503 1129614239 16728 20243 25123 1952 12991 19964 11201 17284 18410 2840 1287724940 4989 21344 23127 3268 15681 23795 2050 16692 25423 4144 9210 10293896 8604 15852 9235 23106 25062 4425 5548 25280 4343 10845 11308 32249603 25270 1859 10301 21895 4944 11025 23373 5530 9419 25244 8525 1589618435 8591 19838 24964 18261 19436 25885 4301 15776 15875 9532 1615820694 9674 11995 20018 8382 9360 12086 2974 19579 25776 2968 4956 207853009 11349 25614 2975 11230 25789

TABLE 9h Address of Parity Bit Accumulators (Rate ½) 1690 4392 724310123 12751 19068 23261 25882 25950 4295 8310 13735 14903 18216 1852120457 22873 26999 2900 6292 14253 16327 19561 21463 23348 26738 311081201 2187 4037 6084 7112 17403 20499 23973 29486 1913 5146 8684 1076211063 15735 19611 22881 27218 1569 1918 5946 8361 9717 12102 16573 1918728309 925 7530 10304 16459 18002 20820 22693 24097 30913 4336 1431516734 16940 19494 19977 21895 25121 31768 3367 3872 10516 11797 1608018647 21646 24129 31143 1557 4179 6997 9985 19179 23292 24350 2683428821 2605 4611 6484 13227 16750 22762 26200 28877 31731 3139 6378 79439983 10171 14917 17887 19560 25630 5706 5916 8409 10080 13664 1375320142 22989 29228 4479 7229 10272 12943 17716 21870 24521 29638 32330818 2084 5177 9571 10713 14061 27997 28946 31914 4223 8466 15465 1624118591 20686 25672 28312 31533 3049 3335 8311 11572 17578 22419 2372427334 27454 607 4010 11542 13746 16393 19392 21126 28048 28409 1687 20904816 6641 7824 8909 10871 25465 30399 1282 3011 6333 8010 10952 1695824124 26242 32302 2156 4900 6829 9255 15769 16823 25927 30541 30839 31335074 7609 10078 13090 15951 22294 27409 28021 588 1624 7313 9206 1290815670 21180 22034 30955 3342 7385 7790 11060 13010 17437 21755 2805228308 3431 5338 15158 18950 23091 24334 26495 28510 30791 515 3366 1186015866 18097 19816 20516 23868 32139 219 6739 12840 20551 23331 2353025670 28997 32168 152 1161 11055 18106 18657 20617 25241 26437 306924846 9453 14029 14862 20321 22192 26263 26518 29656 3613 6463 1222915428 17644 19554 20150 27965 31614 110 6876 9265 14936 18681 31853 366116313 30499 271 6718 20110 21531 29984 30553 1164 17609 23628 8154 1338224492 3653 10000 31610 2337 21448 28080 11999 15213 25875 12821 3128631518 6097 17194 24909 9702 24304 28525 5883 18252 26861 16032 1783420825 8986 16741 21021 568 27281 27400 13853 15558 19265 1005 5259 1224310050 23589 27597 758 7779 12074 2783 12248 14536 810 1354 27229 636220993 27191 10553 18772 30110 2402 2835 21129 12261 15601 22445 1144215365 22496 9669 16977 21706 5711 13362 23591 17344 21970 29298 24013300 29750 12151 27394 32351 2346 25180 25427 2473 16162 20178 37727888 29067 4813 22325 26724 5566 11255 14096 11274 26442 28451 573314961 21477 9204 11769 32017 4994 8043 9090 5419 10606 24702 7182 1124314543 13457 24507 29332 7082 21960 26549 13422 17659 31308 4351 3002630998 11180 13085 17157 18933 21543 23781 14066 18961 22375 8255 1238819309 2529 12598 29636 8811 28673 31573 8938 24504 30413 14629 2490630234 14478 24007 30182 2559 14678 29540 25088 25451 28782 553 2550729461

TABLE 9i Address of Parity Bit Accumulators (Rate ⅖) 4173 6386 681315139 16380 22095 22454 24964 26820 27326 30289 32188 826 1264 3864 77789667 17876 20474 21361 24378 24599 28142 33137 229 1256 4395 6290 666415376 17436 19340 19463 28818 33008 36039 3801 8483 10585 12292 1341814753 17085 18901 21746 22945 35570 37330 1056 7871 8934 9916 1213117573 20277 23395 30197 33313 35985 37827 367 6393 7261 12313 1695618789 19865 22650 23639 24535 31056 36744 4276 10788 13433 16512 1738420031 26177 27799 29564 30931 33354 37567 1446 3707 5576 7649 9769 1172315461 19981 23591 30056 34358 36599 4336 4879 6768 8836 11153 1616318737 26233 28194 29209 32440 36228 4993 6006 9212 11740 14173 1652624459 25254 29745 33408 36055 36434 664 2361 9581 15385 18970 2068322481 25313 25573 28771 29109 38646 60 4096 7203 9634 13663 17240 2206922446 25032 35038 36150 37117 531 2834 6551 13051 17419 18553 2146423928 26936 29707 32040 37070 1518 2753 6081 6875 9167 10435 12956 2011723116 24850 32134 38490 3408 7120 7440 10653 12980 16264 21753 2801029934 31090 32798 37138 1625 2003 12165 12307 18588 19634 22220 2404724332 32481 32815 36389 43 5869 9888 13215 14897 16193 17231 19751 2840334240 37503 37977 995 8360 11257 11794 14564 20565 24887 27011 2937231511 36783 37169 1807 2320 5317 5423 14505 18577 20893 27636 3086533909 37026 38577 2917 3575 8016 11563 15569 17766 20889 24069 2434135063 38343 38694 127 2839 6382 9940 11027 12217 14285 27540 27894 3119931358 34474 1933 4300 6891 13497 16865 20989 22027 28776 29073 3224833905 38280 1378 3266 8115 10258 14509 21738 25522 25610 28824 2936231876 33896 849 7607 10285 10474 12436 16182 19495 21673 29264 3270635784 38261 18317 32445 34841 3016 3492 27531 11220 27356 31589 1421319144 37905 17819 20378 21592 25822 27680 28748 11051 18497 31183 875922683 30156 8604 15941 32844 19298 23156 30575 21482 28103 37945 21425436 35950 2977 10390 20959 1436 7104 12063 14316 22841 36453 4795 1510725769 4674 5422 31791 3026 11082 34646 13803 18011 35474 22733 3361734598 2430 11376 17648 19089 27031 33569 3748 31787 38672 1716 2854130394 18278 33786 34836 8313 26157 32033 2619 34491 37580 31387 3383435739 5034 11365 26172 24580 30460 33982 4375 14974 34935 6085 815925482 12728 23556 35511 2361 35221 35496 7948 15663 37449 12946 1302623162 9367 13954 16799 15553 18209 29641 9304 24815 26869 5095 2663930677 14012 20605 23633 12915 13984 30821 9349 16778 23849 16874 2654126754 15642 20257 28066 7505 14992 20745 547 5328 26296 5178 8851 26552

TABLE 9j Address of Parity Bit Accumulators (Rate ⅓) 7127 12217 1490317792 19690 23709 26904 31847 32174 37971 39934 43192 631 3892 3961 71109168 14664 20881 33763 34077 38290 38589 40587 1561 4952 12735 1705017363 23114 23432 26431 30725 34201 38679 41775 3120 6362 9346 1020219293 21581 26158 28110 28791 30854 37723 39609 937 3213 3271 8272 903515349 18735 23617 27626 33046 35819 42715 42 5281 15192 15731 2068723236 29529 31564 32442 35605 36703 42323 3415 5078 7595 8830 1629816735 18395 18860 20659 21190 24417 39339 1247 3506 4592 7574 1179914188 22214 27862 31190 33446 39010 39447 659 6732 8711 10845 1496720932 21392 24561 27950 30282 34491 39662 1574 6084 6401 10616 1549621480 22587 24801 28997 34755 40468 40765 1816 5243 8287 9380 1279513208 22838 23280 31453 35837 36957 38620 2526 5720 11010 12022 1520019448 27202 27673 29334 32919 36071 42350 542 3767 8589 14736 1759918679 20408 29296 37332 38338 40657 42203 1274 6050 11401 13088 1427117551 31621 32620 36895 37191 39291 43194 312 4625 6259 6839 10672 1669521781 27493 27928 31056 33505 41398 167 1811 6813 10155 10651 1554416043 23824 28470 32607 35112 37845 2477 2675 8067 19670 22707 2706929018 30917 33456 37625 40865 42750 2232 8590 13476 14000 16942 2302623964 26975 29689 33460 36770 41758 2199 4775 7747 8795 17270 1886621982 24102 29704 34123 34954 41148 2130 4709 11954 12300 19938 2529925579 28797 30414 36228 36617 42694 1336 22318 25169 18630 24904 2607119828 24680 29215 33916 41065 41539 14761 30074 40827 10013 20112 2593214530 21735 41427 12985 26680 37635 7003 9909 14113 16556 18312 2060618051 19132 21794 4506 10959 16641 13543 16372 29889 9717 22665 3732430086 36117 40152 19395 33829 38170 3120 17782 40104 1599 30981 352935514 10349 25365 5646 10000 25213 5839 12560 41786 20495 31791 347104251 31730 33042 1029 12241 28921 4009 32368 35306 7216 13773 3649512623 22397 34316 20441 24199 41893 15962 17883 25624 13355 13717 3566724883 27266 28103 24291 28357 34576 964 35256 39973 11315 18036 391202832 16014 25615 3789 7400 11418 9383 32137 37908 11721 30386 39012 796326523 43088 7442 11584 26585

TABLE 9k Address of Parity Bit Accumulators (Rate ¼) 4154 7271 1860826981 29145 30753 34895 36931 37422 42768 47366 47722 3011 5069 61569587 12589 20148 33306 36809 37089 44032 45205 48468 39 1332 8129 1965021273 25443 26292 28737 31676 33999 34500 38260 2180 2761 8052 1075016919 18907 23210 24269 26621 34815 39889 43751 1473 1960 13924 2141023195 27618 32955 36079 38702 41888 44387 44654 4943 6550 9829 1489315444 19815 24320 29734 33955 36141 42602 45015 1132 3914 6903 1215412305 16298 20487 25855 29304 32150 39228 47188 880 8771 13199 1596521881 22783 25410 28163 31814 34217 38887 40142 2890 7245 11208 1876121093 26680 31955 38349 40180 43274 43710 46286 296 571 2760 9305 1352914589 17815 28360 30693 33015 35716 39781 3678 9475 12627 13894 1626719135 22641 24756 28788 33357 35290 46414 2066 9907 11657 15142 1551621000 22945 27012 29663 40795 44925 47884 713 4869 6526 10360 1492021797 31226 35575 41795 42905 45382 45984 1015 4061 6411 8415 1149413574 23760 24879 27137 37539 42259 45488 8455 11853 14155 16832 1931819778 27886 28893 36425 41079 43947 48266 5393 17152 43557 17300 2504448036 25767 28037 31468 4322 42152 44324 27676 46770 47870 23456 2479130363 7899 10123 45744 7716 12923 33714 18718 30285 40475 1794 1803532276 26277 33598 38109 8757 21965 40705 7007 12090 17815 17010 2201037440 3493 13085 32557 10988 18098 20180 2166 11137 23546 15518 2055035071 26272 41471 46610 4430 14274 35788 23839 29219 43155 17336 2077032566 10570 16186 35139 5836 22534 38783 5863 36391 41378 5580 3097141722 5558 30075 39521 14465 39539 40407 3369 30151 46801 9211
 3788046862.


10. A method according to claim 9, wherein row indices of 1's in acolumn index j*M (j=0, 1, 2, 3, . . . , k_(ldpc)/M−1) of the paritycheck matrix are given at the j^(th) row according to the one Table. 11.A method according to claim 9, wherein the LDPC code is of a structurethat facilitates use of a plurality of parallel engines for decoding theencoded signal.
 12. A method according to claim 9, further comprising:modulating the LDPC encoded signal according to a signal constellationreflecting one of QPSK (Quadrature Phase Shift Keying), OQPSK (OffsetQPSK), PSK (Phase Shift Keying), 8-PSK, 16-APSK (Amplitude PSK), and32-APSK.
 13. A method according to claim 9, further comprising:modulating the encoded LDPC signal according to a signal constellationthat comprises a one of the following formats (where ε_(x) representsaverage energy per symbol), a QPSK (Quadrature Phase Shift Keying)constellation having bit labeling and x-y bit positioning according tothe following table: Bit Label [x, y] Coordinates 00 [{square root over(ε_(x))} * cos(π/4.0), {square root over (ε_(x))} * sin(π/4.0)] 01[{square root over (ε_(x))} * cos(7.0 * π/4.0), {square root over(ε_(x))} * sin(7.0 * π/4.0)] 10 [{square root over (ε_(x))} * cos(3.0 *π/4.0), {square root over (ε_(x))} * sin(3.0 * π/4.0)] 11 [{square rootover (ε_(x))} * cos(5.0 * π/4.0), {square root over (ε_(x))} * sin(5.0 *π/4.0)]

an 8-PSK (Phase Shift Keying) constellation having bit labeling and x-ybit positioning according to the following table: Bit Label [x, y]Coordinates 000 [{square root over (ε_(x))} * cos(π/8.0), {square rootover (ε_(x))} * sin(π/8.0)] 001 [{square root over (ε_(x))} * cos(15.0 *π/8.0), {square root over (ε_(x))} * sin(15.0 * π/8.0)] 010 [{squareroot over (ε_(x))} * cos(7.0 * π/8.0), {square root over (ε_(x))} *sin(7.0 * π/8.0)] 011 [{square root over (ε_(x))} * cos(9.0 * π/8.0),{square root over (ε_(x))} * sin(9.0 * π/8.0)] 100 [{square root over(ε_(x))} * cos(3.0 * π/8.0), {square root over (ε_(x))} * sin(3.0 *π/8.0)] 101 [{square root over (ε_(x))} * cos(13.0 * π/8.0), {squareroot over (ε_(x))} * sin(13.0 * π/8.0)] 110 [{square root over(ε_(x))} * cos(5.0 * π/8.0), {square root over (ε_(x))} * sin(5.0 *π/8.0)] 111 [{square root over (ε_(x))} * cos(11.0 * π/8.0), {squareroot over (ε_(x))} * sin(11.0 * π/8.0)]

a 16-APSK (Amplitude Phase Shift Keying) constellation, of a 4+12bit/ring format, having bit labeling and x-y bit positioning accordingto the following table (where R1 represents the radius of an inner ringand R2 represents the radius of an outer ring, and 4*R1²+12*R2²=16): BitLabel [x, y] Coordinates 0000 [R2 * {square root over (ε_(x))} *cos(3.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(3.0 * π/12.0)]0001 [R2 * {square root over (ε_(x))} * cos(21.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(21 * π/12.0)] 0010 [R2 * {square root over(ε_(x))} * cos(9.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(9 *π/12.0)] 0011 [R2 * {square root over (ε_(x))} * cos(15.0 * π/12.0),R2 * {square root over (ε_(x))} * sin(15 * π/12.0)] 0100 [R2 * {squareroot over (ε_(x))} * cos(π/12.0), R2 * {square root over (ε_(x))} *sin(π/12.0)] 0101 [R2 * {square root over (ε_(x))} * cos(23.0 * π/12.0),R2 * {square root over (ε_(x))} * sin(23 * π/12.0)] 0110 [R2 * {squareroot over (ε_(x))} * cos(11.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(11 * π/12.0)] 0111 [R2 * {square root over (ε_(x))} *cos(13.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(13 * π/12.0)]1000 [R2 * {square root over (ε_(x))} * cos(5.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(5 * π/12.0)] 1001 [R2 * {square root over(ε_(x))} * cos(19.0 * π/12.0), R2 * {square root over (ε_(x))} *sin(19 * π/12.0)] 1010 [R2 * {square root over (ε_(x))} * cos(7.0 *π/12.0), R2 * {square root over (ε_(x))} * sin(7 * π/12.0)] 1011 [R2 *{square root over (ε_(x))} * cos(17.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(17 * π/12.0)] 1100 [R1 * {square root over (ε_(x))} *cos(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 1101 [R1 *{square root over (ε_(x))} * cos(7.0 * π/4.0), R1 * {square root over(ε_(x))} * sin(7.0 * π/4.0)] 1110 [R1 * {square root over (ε_(x))} *cos(3.0 * π/4.0), R1 * {square root over (ε_(x))} * sin(3.0 * π/4.0)]1111 [R1 * {square root over (ε_(x))} * cos(5.0 * π/4.0), R1 * {squareroot over (ε_(x))} * sin(5.0 * π/4.0)]

a 32-APSK constellation, of a 4+12+16 bit/ring format, having bitlabeling and x-y bit positioning according to the following table (whereR1 represents the radius of an inner ring, R2 represents the radius of amiddle ring and R3 represents the radius of an outer ring, and4*R1²+12*R2²+16*R3²=32): Bit Label [x, y] Coordinates 00000 [R2 *{square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00001 [R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00010[R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 00011 [R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00100[−R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00110[−R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 00111 [−R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 01000[R3 * {square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 01001 [R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 01010 [R3 *{square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 01011 [0, −R3 * {square root over (ε_(x))}] 01100[−R3 * {square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 01101 [0, R3 * {square root over (ε_(x))}] 01110[−R3 * {square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 01111 [−R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 10000 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 10001 [R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10010 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over(ε_(x))} * sin(π/12.0)] 10011 [R1 * {square root over (ε_(x))} *sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)] 10100 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 10101 [−R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10110 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over(ε_(x))} * sin(π/12.0)] 10111 [−R1 * {square root over (ε_(x))} *sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)] 11000 [R3 *{square root over (ε_(x))}, 0] 11001 [R3 * {square root over (ε_(x))} *sin(π/4.0), R3 * {square root over (ε_(x))} * sin(π/4.0)] 11010 [R3 *{square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 11011 [R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 11100 [−R3 *{square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 11101 [−R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 11110 [−R3 *{square root over (ε_(x))}, 0] 11111 [−R3 * {square root over (ε_(x))} *sin(π/4.0), −R3 * {square root over (ε_(x))} * sin(π/4.0)]

a 32-APSK constellation, of a 4+12+16 bit/ring format, having bitlabeling and x-y bit positioning according to the following table (whereR1 represents the radius of an inner ring, R2 represents the radius of amiddle ring and R3 represents the radius of an outer ring, and4*R1²+12*R2²+16*R3²=32): Bit Label [x, y] Coordinates 00000 [−R3 *{square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 00001 [−R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 00010 [R3 *{square root over (ε_(x))} * sin(π/8.0), R3 * {square root over(ε_(x))} * cos(π/8.0)] 00011 [0, R3 * {square root over (ε_(x))}] 00100[−R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * ε_(x) * sin(5.0 * π/12.0)] 00110 [R2 * {square rootover (ε_(x))} * sin(π/4.0), R2 * {square root over (ε_(x))} *sin(π/4.0)] 00111 [R2 * {square root over (ε_(x))} * sin(π/12.0), R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0)] 01000 [−R3 * {squareroot over (ε_(x))} * cos(π/8.0), R3 * {square root over (ε_(x))} *sin(π/8.0)] 01001 [−R3 * {square root over (ε_(x))}, 0] 01010 [R3 *{square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 01011 [R3 * {square root over (ε_(x))} *cos(π/8.0), R3 * {square root over (ε_(x))} * sin(π/8.0)] 01100 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 01101 [−R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 01110 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/2.0)] 01111 [R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10000 [−R3 *{square root over (ε_(x))} * sin(π/8.0), −R3 * {square root over(ε_(x))} * cos(π/8.0)] 10001 [0, −R3 * {square root over (ε_(x))}] 10010[R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 10011 [R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 10100 [−R2 *{square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 10101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 10110[R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 10111 [R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 11000[−R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 11001 [−R3 * {square root over (ε_(x))} *cos(π/8.0), −R3 * {square root over (ε_(x))} * sin(π/8.0)] 11010 [R3 *{square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 11011 [R3 * {square root over (ε_(x))}, 0] 11100[−R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {squareroot over (ε_(x))} * sin(π/12.0)] 11101 [−R1 * {square root over(ε_(x))} * sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)]11110 [R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 *{square root over (ε_(x))} * sin(π/12.0)] 11111 [R1 * {square root over(ε_(x))} * sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)].


14. A method according to claim 9, further comprising: encoding, priorto the LDPC encoding, the one or more blocks of information bits of thesource signal based on a t-error Bose Chaudhuri Hocquenghem (BCH) code.15. A method according to claim 14, further comprising: interleaving theLDPC encoded signal.
 16. A method according to claim 15, furthercomprising: modulating the interleaved signal according to a signalconstellation that comprises a one of the following formats (where ε_(x)represents average energy per symbol), a QPSK (Quadrature Phase ShiftKeying) constellation having bit labeling and x-y bit positioningaccording to the following table: Bit Label [x, y] Coordinates 00[{square root over (ε_(x))} * cos(π/4.0), {square root over (ε_(x))} *sin(π/4.0)] 01 [{square root over (ε_(x))} * cos(7.0 * π/4.0), {squareroot over (ε_(x))} * sin(7.0 * π/4.0)] 10 [{square root over (ε_(x))} *cos(3.0 * π/4.0), {square root over (ε_(x))} * sin(3.0 * π/4.0)] 11[{square root over (ε_(x))} * cos(5.0 * π/4.0), {square root over(ε_(x))} * sin(5.0 * π/4.0)]

an 8-PSK (Phase Shift Keying) constellation having bit labeling and x-ybit positioning according to the following table: Bit Label [x, y]Coordinates 000 [{square root over (ε_(x) )}* cos(π/8.0), {square rootover (ε_(x) )}* sin(π/8.0)] 001 [{square root over (ε_(x) )}* cos(15.0 *π/8.0), {square root over (ε_(x) )}* sin(15.0 * π/8.0)] 010 [{squareroot over (ε_(x) )}* cos(7.0 * π/8.0), {square root over (ε_(x) )}*sin(7.0 * π/8.0)] 011 [{square root over (ε_(x) )}* cos(9.0 * π/8.0),{square root over (ε_(x) )}* sin(9.0 * π/8.0)] 100 [{square root over(ε_(x) )}* cos(3.0 * π/8.0), {square root over (ε_(x) )}* sin(3.0 *π/8.0)] 101 [{square root over (ε_(x) )}* cos(13.0 * π/8.0), {squareroot over (ε_(x) )}* sin(13.0 * π/8.0)] 110 [{square root over (ε_(x))}* cos(5.0 * π/8.0), {square root over (ε_(x) )}* sin(5.0 * π/8.0)] 111[{square root over (ε_(x) )}* cos(11.0 * π/8.0), {square root over(ε_(x) )}* sin(11.0 * π/8.0)]

a 16-APSK (Amplitude Phase Shift Keying) constellation, of a 4+12bit/ring format, having bit labeling and x-y bit positioning accordingto the following table (where R1 represents the radius of an inner ringand R2 represents the radius of an outer ring, and 4*R1²+12*R2²=16): BitLabel [x, y] Coordinates 0000 [R2 * {square root over (ε_(x))} *cos(3.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(3.0 * π/12.0)]0001 [R2 * {square root over (ε_(x))} * cos(21.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(21 * π/12.0)] 0010 [R2 * {square root over(ε_(x))} * cos(9.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(9 *π/12.0)] 0011 [R2 * {square root over (ε_(x))} * cos(15.0 * π/12.0),R2 * {square root over (ε_(x))} * sin(15 * π/12.0)] 0100 [R2 * {squareroot over (ε_(x))} * cos(π/12.0), R2 * {square root over (ε_(x))} *sin(π/12.0)] 0101 [R2 * {square root over (ε_(x))} * cos(23.0 * π/12.0),R2 * {square root over (ε_(x))} * sin(23 * π/12.0)] 0110 [R2 * {squareroot over (ε_(x))} * cos(11.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(11 * π/12.0)] 0111 [R2 * {square root over (ε_(x))} *cos(13.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(13 * π/12.0)]1000 [R2 * {square root over (ε_(x))} * cos(5.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(5 * π/12.0)] 1001 [R2 * {square root over(ε_(x))} * cos(19.0 * π/12.0), R2 * {square root over (ε_(x))} *sin(19 * π/12.0)] 1010 [R2 * {square root over (ε_(x))} * cos(7.0 *π/12.0), R2 * {square root over (ε_(x))} * sin(7 * π/12.0)] 1011 [R2 *{square root over (ε_(x))} * cos(17.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(17 * π/12.0)] 1100 [R1 * {square root over (ε_(x))} *cos(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 1101 [R1 *{square root over (ε_(x))} * cos(7.0 * π/4.0), R1 * {square root over(ε_(x))} * sin(7.0 * π/4.0)] 1110 [R1 * {square root over (ε_(x))} *cos(3.0 * π/4.0), R1 * {square root over (ε_(x))} * sin(3.0 * π/4.0)]1111 [R1 * {square root over (ε_(x))} * cos(5.0 * π/4.0), R1 * {squareroot over (ε_(x))} * sin(5.0 * π/4.0)]

a 32-APSK constellation, of a 4+12+16 bit/ring format, having bitlabeling and x-y bit positioning according to the following table (whereR1 represents the radius of an inner ring, R2 represents the radius of amiddle ring and R3 represents the radius of an outer ring, and4*R1²+12*R2²+16*R3²=32): Bit Label [x, y] Coordinates 00000 [R2 *{square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00001 [R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00010[R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 00011 [R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00100[−R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00110[−R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 00111 [−R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 01000[R3 * {square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 01001 [R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 01010 [R3 *{square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 01011 [0, −R3 * √ε_(x)] 01100 [−R3 * {square rootover (ε_(x))} * sin(π/4.0), R3 * {square root over (ε_(x))} *sin(π/4.0)] 01101 [0, R3 * √ε_(x)] 01110 [−R3 * {square root over(ε_(x))} * cos(π/8.0), −R3 * {square root over (ε_(x))} * sin(π/8.0)]01111 [−R3 * {square root over (ε_(x))} * sin(π/8.0), −R3 * {square rootover (ε_(x))} * cos(π/8.0)] 10000 [R2 * {square root over (ε_(x))} *sin(5.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(π/12.0)] 10001[R1 * {square root over (ε_(x))} * sin(π/4.0), R1 * {square root over(ε_(x))} * sin(π/4.0)] 10010 [R2 * {square root over (ε_(x))} *sin(5.0 * π/12.0), −R2 * {square root over (ε_(x))} * sin(π/12.0)] 10011[R1 * {square root over (ε_(x))} * sin(π/4.0), −R1 * {square root over(ε_(x))} * sin(π/4.0)] 10100 [−R2 * {square root over (ε_(x))} *sin(5.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(π/12.0)] 10101[−R1 * {square root over (ε_(x))} * sin(π/4.0), R1 * {square root over(ε_(x))} * sin(π/4.0)] 10110 [−R2 * {square root over (ε_(x))} *sin(5.0 * π/12.0), −R2 * {square root over (ε_(x))} * sin(π/12.0)] 10111[−R1 * {square root over (ε_(x))} * sin(π/4.0), −R1 * {square root over(ε_(x))} * sin(π/4.0)] 11000 [R3 * √ε_(x), 0] 11001 [R3 * {square rootover (ε_(x))} * sin(π/4.0), R3 * {square root over (ε_(x))} *sin(π/4.0)] 11010 [R3 * {square root over (ε_(x))} * cos(π/8.0), −R3 *{square root over (ε_(x))} * sin(π/8.0)] 11011 [R3 * {square root over(ε_(x))} * sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)]11100 [−R3 * {square root over (ε_(x))} * cos(π/8.0), R3 * {square rootover (ε_(x))} * sin(π/8.0)] 11101 [−R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 11110 [−R3 *√ε_(x), 0] 11111 [−R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 *{square root over (ε_(x))} * sin(π/4.0)]

a 32-APSK constellation, of a 4+12+16 bit/ring format, having bitlabeling and x-y bit positioning according to the following table (whereR1 represents the radius of an inner ring, R2 represents the radius of amiddle ring and R3 represents the radius of an outer ring, and4*R1²+12*R2²+16*R3²=32): Bit Label [x, y] Coordinates 00000 [−R3 *{square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 00001 [−R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 00010 [R3 *{square root over (ε_(x))} * sin(π/8.0), R3 * {square root over(ε_(x))} * cos(π/8.0)] 00011 [0, R3 * √ε_(x)] 00100 [−R2 * {square rootover (ε_(x))} * sin(π/4.0), R2 * {square root over (ε_(x))} *sin(π/4.0)] 00101 [−R2 * {square root over (ε_(x))} * sin(π/12.0), R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0)] 00110 [R2 * {square rootover (ε_(x))} * sin(π/4.0), R2 * {square root over (ε_(x))} *sin(π/4.0)] 00111 [R2 * {square root over (ε_(x))} * sin(π/12.0), R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0)] 01000 [−R3 * {squareroot over (ε_(x))} * cos(π/8.0), R3 * {square root over (ε_(x))} *sin(π/8.0)] 01001 [−R3 * √ε_(x), 0] 01010 [R3 * {square root over(ε_(x))} * sin(π/4.0), R3 * {square root over (ε_(x))} * sin(π/4.0)]01011 [R3 * {square root over (ε_(x))} * cos(π/8.0), R3 * {square rootover (ε_(x))} * sin(π/8.0)] 01100 [−R2 * {square root over (ε_(x))} *sin(5.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(π/12.0)] 01101[−R1 * {square root over (ε_(x))} * sin(π/4.0), R1 * {square root over(ε_(x))} * sin(π/4.0)] 01110 [R2 * {square root over (ε_(x))} *sin(5.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(π/12.0)] 01111[R1 * {square root over (ε_(x))} * sin(π/4.0), R1 * {square root over(ε_(x))} * sin(π/4.0)] 10000 [−R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 10001 [0,−R3 * √ε_(x)] 10010 [R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 *{square root over (ε_(x))} * sin(π/4.0)] 10011 [R3 * {square root over(ε_(x))} * sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)]10100 [−R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square rootover (ε_(x))} * sin(π/4.0)] 10101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 10110[R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 10111 [R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 11000[−R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 11001 [−R3 * {square root over (ε_(x))} *cos(π/8.0), −R3 * {square root over (ε_(x))} * sin(π/8.0)] 11010 [R3 *{square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 11011 [R3 * √ε_(x), 0] 11100 [−R2 * {square rootover (ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over (ε_(x))} *sin(π/12.0)] 11101 [−R1 * {square root over (ε_(x))} * sin(π/4.0), −R1 *{square root over (ε_(x))} * sin(π/4.0)] 11110 [R2 * {square root over(ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over (ε_(x))} *sin(π/12.0)] 11111 [R1 * {square root over (ε_(x))} * sin(π/4.0), −R1 *{square root over (ε_(x))} * sin(π/4.0)].


17. An apparatus, comprising: at least one processor; and at least onememory including computer program code for one or more programs, the atleast one memory and the computer program code configured to, with theat least one processor, cause the apparatus to perform at least thefollowing: accessing stored information representing a predeterminedstructured parity check matrix of a Low Density Parity Check (LDPC)code, wherein the stored information reflects a tabular format of rowsand columns, wherein each row represents occurrences of one valueswithin a respective column of the parity check matrix, and wherein thecolumns of the parity check matrix are derived according to apredetermined operation based on the respective rows of the storedtabular information; and encoding one or more blocks of information bitsof a source signal based on the LDPC code to generate an LDPC encodedsignal; wherein the LDPC encoding of the blocks of information bits(each block being of a size of k_(ldpc) information bits, and eachresulting encoded block being of a size of n_(ldpc) code bits includingparity bits p_(i), i=0, 1, 2, . . . , n_(ldpc)−k_(ldpc)−1), comprises:initializing parity bit accumulators a₀=a₁= . . . =a_(n) _(ldpc) _(−k)_(ldpc) ⁻¹=0; for a one of the blocks of information bits, divided intoj sequential groups (each of a size of M information bits), and for j=1,2, 3, . . . k_(ldpc)/M: (1) accumulating a first information bit of aj^(th) group in certain of the parity bit accumulators reflected byaccumulator addresses based on a j^(th) row of the stored tabularinformation; and (2) accumulating the remaining (M−1) information bitsof the j^(th) group in certain of the parity bit accumulators reflectedby accumulator addresses according to {x+m mod M*q}mod(n_(ldpc)−k_(ldpc)), wherein x denotes an address of the parity bitaccumulator corresponding to the first bit of the group, andq=(n_(ldpc)−k_(ldpc))/M; and after all of the information bits of theone block are accumulated, sequentially performing operations (withrespect to the parity bit accumulators) according toa_(i)=a_(i)⊕a_(i-1), i=1, 2, . . . (n_(ldpc)−k_(ldpc)−1), where theadditions are in Galois Field (GF) 2; and wherein the parity bits p_(i),i=0, 1, . . . (n_(ldpc)−k_(ldpc)−1) are respectively reflected by theresulting parity bit accumulators a_(i), i=0, 1, . . .(n_(ldpc)−k_(ldpc)−1); and wherein the stored information representingthe structured parity check matrix comprises a one of the followingTables 17a through 17r, TABLE 17a Address of Parity Bit Accumulators(Rate 9/10 - Coded Block Size 720) 10 62 53 15 54 56 5 3 8 34 23 45 1060 23 27 6 70 51 65 26 38 23 67 18 22 25 1 12 28 5 61 36 44 7 49 20 4629 69 6 22 31 46 37 51 54 18 65 32 11 17 46 32 15 0 3 45 44 24 63 64 4523

TABLE 17b Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 960) 88 70 81 43 6 64 29 13 18 82 1 35 10 6 47 53 38 22 57 1 78 687 15 78 48 73 37 26 82 13 17 52 62 19 29 58 14 79 27 86 16 19 2 7 95 4430 5 42 81 13 22 66 17 8 93 19 82 50 41 16 93 57

TABLE 17c Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 1440) 132 109 122 67 12 97 46 19 120 129 70 31 28 125 2 55 108 81134 59 136 49 30 139 40 69 38 123 100 141 46 75 64 109 134 47 120 29 2667 112 37 10 55 136 53 122 103 80 17 34 115 40 61 46 71 132 81 18 7 12113 6 143 108 113 122 11 108 69 110 63 124 141 2 115 100 133 18 15 133 051 106 40 115 101 62 67 136 17 50 80 10 75 37 126 19 40 25 122 40 129143 12 66 83 17 7 74 52 17 23 8 21 94 117 119 80 70 104 25 66 43 73 8898 111

TABLE 17d Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 2160) 36 153 142 127 136 157 182 151 108 197 106 63 108 49 182 35 889 134 43 56 105 30 175 104 181 66 115 96 5 78 211 52 57 194 119 128 972 23 196 37 2 171 184 177 10 15 56 17 2 43 84 121 142 35 8 21 62 107 184193 46 7 160 205 42 107 120 181 122 103 196 153 46 163 72 105 202 11 3186 157 176 186 129 0 27 201 140 154 191 155 6 105 124 118 55 44 197 8760 189 206 121 8 215 206 93 43 136 94 65 28 178 51 110 59 144 149 98 12149 107 184 61 122 99

TABLE 17e Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 2880) 92 133 95 39 78 91 251 284 262 92 89 204 15 226 74 150 73 3928 47 258 175 57 160 171 286 97 12 208 69 108 59 164 4 171 217 50 245171 139 18 122 35 97 30 26 160 53 81 72 286 20 236 259 66 105 11 0 146 7196 95 168 194 1 129 64 29 241 177 250 47 151 53 184 192 59 52 21 84 24887 264 280 103 278 137 154 175 56 273 192 43 80 183 95 134 245 142 33229 18 196 200 186 188 251 33 43 33 250 74 6 55 77 261 282 139 286 227135 163 89 252 151 250 138 286 205 32 137 4 44 87 137 192 158 189 138 50173 236 15 94 82 285 281 133 249 191 114 1 128 96 193 76 1 242 153 284156 53 42 92 160 113 247 81 196 275 103 168 117 262 116 166 137 177 8125 115 9 6 199 219 18 208 138 73 14 154 101

TABLE 17f Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 3600) 212 271 274 5 122 345 127 59 138 71 189 157 60 256 26 143 234105 190 224 240 217 129 58 135 2 349 221 227 336 171 194 358 169 77 33034 235 174 269 74 261 28 235 126 50 345 130 302 42 31 15 214 47 79 33989 180 178 9 38 192 89 49 332 256 222 183 187 140 88 137 213 307 190 137225 258 289 233 188 336 85 93 98 352 333 17 324 62 244 149 108 19 242292 340 303 65 150 166 95 282 169 278 61 113 234 122 207 52 107 37 296135 178 330 271 200 339 176 243 203 284 202 249 210 350 9 61 126 16 253317 108 91 298 287 160 237 31 72 247 124 38 347 169 113 346 24 266 21108 188 267 269 298 117 275 332 216 163 317 130 146 272 82 193 30 129 77282 7 327 292 319 5 99 276 305 125 169 303 80 225 60 92 304 7 36 86 46

TABLE 17g Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 4320) 273 190 207 371 331 258 135 416 306 12 291 293 262 215 396 7414 193 91 207 384 341 260 81 128 365 170 9 336 396 413 238 16 407 130 442 323 54 85 6 103 349 176 216 286 426 277 425 416 419 322 289 164 379189 1 292 319 363 345 132 134 423 366 146 381 235 88 111 206 4 121 426307 254 203 244 406 216 7 275 53 76 329 418 416 84 233 293 351 368 153410 101 183 196 400 170 65 192 357 31 43 46 245 428 304 51 1 144 351 319321 413 298 350 213 244 210 387 166 367 228 297 178 83 238 97 428 266165 197 423 115 265 43 104 172 122 144 227 407 65 166 210 73 311 94 351154 357 64 172 30 13 320 243 412 318 392 346 252 286 13 207 208 277 17867 161 394 351 45 17 295 196 251 326 356 145 168 411 262 54 51 177 398148 355 330 168 399 161 312 50 419 65 327 61 374 232 28 69 303 298 116221 52 270 165 103 398 283 243 184 364 348 7 209 362 221 187 343 184 190265 306 277 56 25 34 325 345 60 198 344 113 68 41 171 253 56 188 431 27256 106 421 22 274 279 67 298 294 79

TABLE 17h Address of Parity Bit Accumulators (Rate 9/10 - Coded BlockSize 5760) 35 247 105 399 280 268 513 68 161 104 460 466 156 253 305 39372 489 178 202 398 199 151 383 92 527 54 224 200 409 42 147 459 569 553312 242 180 155 10 216 458 361 318 104 489 206 52 22 56 123 538 264 295130 29 263 28 274 239 276 124 449 21 360 482 519 253 225 202 212 312 268338 558 200 43 291 436 27 84 231 40 521 95 142 558 361 475 462 319 41984 74 522 573 451 188 526 263 226 159 440 491 415 434 60 215 553 250 72209 18 436 311 210 327 524 536 18 15 211 11 453 22 452 289 305 351 187343 240 98 33 493 147 100 176 188 384 379 347 349 332 532 518 483 445496 203 269 304 459 344 311 574 128 429 538 527 479 125 43 508 228 315416 231 417 558 501 190 498 526 341 505 270 381 517 260 12 481 91 44 540104 339 295 172 467 569 121 137 474 221 567 444 506 104 526 327 547 134519 522 262 547 37 375 377 455 400 327 325 213 390 6 167 11 363 160 541337 185 61 225 7 233 450 407 323 288 38 463 95 274 279 377 423 411 227558 156 114 497 471 22 73 296 508 393 182 304 239 183 415 322 332 28 500106 470 358 505 461 302 342 68 255 90 416 368 487 177 531 161 84 314 391310 392 367 177 19 102 130 366 25

TABLE 17i Address of Parity Bit Accumulators (Rate ⅔ - Coded Block Size1080) 78 323 226 335 169 288 12 213 328 321 122 163 12 37 310 223 344 97346 195 180 325 22 311 56 121 26 187 148 109 302 119 332 251 289 166 19724 303 313 258 228 239 181 232 154 323 182 6 282 77 162 3 199 295 112251 33 50 61 139 208 95 228 121 216 356 302 349 201 324 14

TABLE 17j Address of Parity Bit Accumulators (Rate ⅘ - Coded Block Size1080) 90 67 188 117 28 125 186 1 146 99 22 197 60 85 44 147 118 41 42133 8 75 142 17 30 97 158 93 46 71 30 109 182 195 16 143 60 10 105 33166 185 142 85 168 86 133 159 104 137 91 24 110 167 31 36 46 142 186 6389 139 116 99 5 88 176 195 193 12 44 185 168 37 146 141 166 101 66 37200 45 136 89 90 19 152 111 94 179 84 211 26 183 64 113 60 1 80 129 190179 6 121 20 159 88 131

TABLE 17k Address of Parity Bit Accumulators (Rate 8/9 - Coded BlockSize 720) 34 78 37 17 72 76 43 35 2 4 79 37 40 60 51 17 4 70 59 49 50 2263 31 46 20 69 73 40 70 57 55 38 22 43 46 40 71 14 17 61 26 21 45 4 36 160 26 33 46 55 21 36 27 13

TABLE 17l Address of Parity Bit Accumulators (Rate 8/9 - Coded BlockSize 1080) 20 77 70 31 96 45 86 3 24 65 34 3 0 21 74 67 28 5 106 71 1641 18 95 72 17 6 59 40 69 22 71 64 101 86 83 96 85 46 119 96 37 70 99 089 46 59 80 65 74 63 44 57 102 79 76 5 54 115 8 109 74 119 32 105 118 4857 62 44 89 30 80 97 114 60 65 115 40 5 111 52 9 27 108 105 79 116 38 4732 38 79 36 34 51 56 94 119 49 114 119 21 78 51 1 22 87 37 66 15

TABLE 17m Address of Parity Bit Accumulators (Rate 8/9 - Coded BlockSize 1440) 68 49 138 87 16 89 62 39 140 1 106 75 12 141 46 67 100 9 2687 12 41 94 83 128 73 106 35 20 113 10 55 16 81 122 135 136 97 38 111140 77 102 143 60 105 86 71 88 61 130 39 136 121 134 75 92 145 98 151 125 50 7 64 125 94 152 9 6 56 9 130 96 93 114 60 93 103 48 157 139 132 157115 72 61 79 64 14 31 80 130 95 140 46 131 92 74 139 5 122 75 145 14 19121 22 143 121 86 119

TABLE 17n Address of Parity Bit Accumulators (Rate 8/9 - Coded BlockSize 2160) 116 121 22 107 120 113 90 115 168 225 70 199 208 137 190 99220 113 34 207 52 177 94 235 204 229 66 171 100 85 218 123 16 113 2 2396 73 26 159 120 169 138 199 104 65 130 139 96 161 194 143 104 209 22639 236 125 182 79 140 13 50 79 28 193 118 188 89 34 224 61 50 128 81 46156 9 111 156 37 175 72 105 239 64 137 131 176 182 135 148 18 95 100 54215 224 174 103 165 238 87 145 214 207 89 182 55 53 38 159

TABLE 17o Address of Parity Bit Accumulators (Rate 8/9 - Coded BlockSize 2880) 33 174 30 142 266 282 240 78 291 229 80 43 156 132 134 303 5031 287 239 68 186 92 75 59 203 255 37 171 139 287 45 101 23 89 52 20 27138 109 84 32 111 225 183 314 101 110 142 163 44 25 206 302 173 5 86 27218 39 237 199 140 86 248 159 56 167 215 283 76 254 190 187 148 291 31057 53 99 90 134 151 199 111 30 227 148 51 167 33 294 190 147 173 84 175108 35 317 138 111 300 73 306 292 224 106 307 274 202 153 79 58 195 13110 249 242 51 9 28 275 6 287 54 246 313 106 88 49 315 42 218 265 212 23985 306 147

TABLE 17p Address of Parity Bit Accumulators (Rate 8/9 - Coded BlockSize 3600) 267 282 5 84 96 78 167 18 276 240 117 303 136 175 169 324 11773 360 4 379 398 265 253 146 11 62 89 114 227 342 31 26 284 295 49 239137 124 350 118 266 191 155 213 310 20 73 384 231 396 323 216 317 150129 232 58 27 245 272 18 59 253 62 376 44 337 293 392 42 396 87 270 9125 284 2 22 157 8 169 355 174 71 330 336 156 11 325 343 265 226 395 101263 163 60 152 303 250 245 206 289 382 354 57 368 212 201 271 214 120237 11 68 362 174 180 269 315 7 233 112 290 11 157 183 351 284 9 95 240233 335 261 152 78 267 348 253 42 75 78 75 29 98 64 84 385 378 54 39 152132 298 41 3 396 171 183 397 328 47 336 197 218 214 19 266 57 166 285265 284 214 75 5 239 74 46 244 313 317 127 8 3 65 50 60 177 310 119 325136 36 134 152 154 59 103 323 245 369 120 148 328 387 21 20 355 13 238384 193 154 351 121 322 390 44 66 326 39

TABLE 17q Address of Parity Bit Accumulators (Rate 8/9 - Coded BlockSize 4320) 30 196 79 344 162 460 169 79 210 252 30 83 389 334 100 47 19911 210 305 344 333 474 454 400 137 475 29 328 137 67 453 228 258 371 168 268 197 38 174 403 56 41 25 52 309 303 239 152 81 379 106 452 443 31474 149 238 119 465 314 349 366 406 458 395 152 229 38 432 457 421 360113 247 244 144 178 315 189 97 212 62 375 166 356 397 2 307 79 436 385314 411 287 159 389 392 190 77 115 316 118 50 284 59 53 329 67 277 42177 466 331 380 144 335 402 52 48 449 126 151 160 273 70 143 53 440 436321 262 469 271 379 374 55 394 181 279 57 168 176 225 134 322 267 220418 203 308 270 332 257 398 82 379 104 167 117 141 82 168 119 332 470370 165 96 361 51 463 225 363 460 468 151 461 103 444 357 359 357 203188 1 350 379 385 256 274 393 123 408 434 142 96 426 414 343 22 106 277434 108 363 110 257 407 85 353 204 45 307 424 39 230 376 41 346 416 259124

TABLE 17r Address of Parity Bit Accumulators (Rate 8/9 - Coded BlockSize 5760) 353 507 64 261 477 315 226 338 72 128 203 524 180 202 549 634189 460 321 307 339 402 117 164 461 342 193 78 145 236 119 63 100 365496 418 210 341 285 136 376 482 304 510 468 31 274 75 587 550 182 409 30365 461 19 184 599 351 66 28 627 2 475 143 352 175 161 163 637 166 15933 138 486 307 580 583 384 8 573 524 380 465 510 366 451 154 93 258 525304 358 286 434 410 458 26 442 565 530 385 548 99 207 142 119 321 177529 372 111 213 517 492 276 71 473 407 479 325 351 298 62 219 368 361476 56 304 558 543 554 515 527 621 379 447 56 482 560 469 205 637 453334 18 500 469 244 395 102 230 593 92 547 160 491 103 266 541 50 233 15677 72 397 39 464 305 68 284 519 307 35 281 349 44 191 275 460 296 232348 543 332 626 40 23 28 31 205 512 476 107 519 60 458 224 9 406 148 341346 442 270 544 283 259 571 503 363 157 472 425 170 107 384 425 288 46786 199 323 564 536 513 10 167 352 500 48 104 432 347 311 392 118 571 396145 584 609 328 145 50 403 181 625 159 73 169 271 265 626 552 327 564439 132 55 384 221 57 75 477 292 598 16 273 148 90 209 266 160 451 98 20143
 274.


18. An apparatus according to claim 17, wherein row indices of 1's in acolumn index j*M (j=0, 1, 2, 3, . . . , k_(ldpc)/M−1) of the paritycheck matrix are given at the j^(th) row according to the one Table. 19.An apparatus according to claim 17, wherein the LDPC code is of astructure that facilitates use of a plurality of parallel engines fordecoding the encoded signal.
 20. An apparatus according to claim 17,wherein the apparatus is further caused to perform the following:modulating the LDPC encoded signal according to a signal constellationreflecting one of QPSK (Quadrature Phase Shift Keying), OQPSK (OffsetQPSK), PSK (Phase Shift Keying), 8-PSK, 16-APSK (Amplitude PSK), and32-APSK.
 21. An apparatus according to claim 17, wherein the apparatusis further caused to perform the following: modulating the LDPC encodedsignal according to a signal constellation that comprises a one of thefollowing formats (where ε_(x) represents average energy per symbol), aQPSK (Quadrature Phase Shift Keying) constellation having bit labelingand x-y bit positioning according to the following table: Bit Label [x,y] Coordinates 00 [{square root over (ε_(x))} * cos(π/4.0), {square rootover (ε_(x))} * sin(π/4.0)] 01 [{square root over (ε_(x))} * cos(7.0 *π/4.0), {square root over (ε_(x))} * sin(7.0 * π/4.0)] 10 [{square rootover (ε_(x))} * cos(3.0 * π/4.0), {square root over (ε_(x))} * sin(3.0 *π/4.0)] 11 [{square root over (ε_(x))} * cos(5.0 * π/4.0), {square rootover (ε_(x))} * sin(5.0 * π/4.0)]

an 8-PSK (Phase Shift Keying) constellation having bit labeling and x-ybit positioning according to the following table: Bit Label [x, y]Coordinates 000 [{square root over (ε_(x))} * cos(π/8.0), {square rootover (ε_(x))} * sin(π/8.0)] 001 [{square root over (ε_(x))} * cos(15.0 *π/8.0), {square root over (ε_(x))} * sin(15.0 * π/8.0)] 010 [{squareroot over (ε_(x))} * cos(7.0 * π/8.0), {square root over (ε_(x))} *sin(7.0 * π/8.0)] 011 [{square root over (ε_(x))} * cos(9.0 * π/8.0),{square root over (ε_(x))} * sin(9.0 * π/8.0)] 100 [{square root over(ε_(x))} * cos(3.0 * π/8.0), {square root over (ε_(x))} * sin(3.0 *π/8.0)] 101 [{square root over (ε_(x))} * cos(13.0 * π/8.0), {squareroot over (ε_(x))} * sin(13.0 * π/8.0)] 110 [{square root over(ε_(x))} * cos(5.0 * π/8.0), {square root over (ε_(x))} * sin(5.0 *π/8.0)] 111 [{square root over (ε_(x))} * cos(11.0 * π/8.0), {squareroot over (ε_(x))} * sin(11.0 * π/8.0)]

a 16-APSK (Amplitude Phase Shift Keying) constellation, of a 4+12bit/ring format, having bit labeling and x-y bit positioning accordingto the following table (where R1 represents the radius of an inner ringand R2 represents the radius of an outer ring, and 4*R1²+12*R2²=16): BitLabel [x, y] Coordinates 0000 [R2 * {square root over (ε_(x))} *cos(3.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(3.0 * π/12.0)]0001 [R2 * {square root over (ε_(x))} * cos(21.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(21 * π/12.0)] 0010 [R2 * {square root over(ε_(x))} * cos(9.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(9 *π/12.0)] 0011 [R2 * {square root over (ε_(x))} * cos(15.0 * π/12.0),R2 * {square root over (ε_(x))} * sin(15 * π/12.0)] 0100 [R2 * {squareroot over (ε_(x))} * cos(π/12.0), R2 * {square root over (ε_(x))} *sin(π/12.0)] 0101 [R2 * {square root over (ε_(x))} * cos(23.0 * π/12.0),R2 * {square root over (ε_(x))} * sin(23 * π/12.0)] 0110 [R2 * {squareroot over (ε_(x))} * cos(11.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(11 * π/12.0)] 0111 [R2 * {square root over (ε_(x))} *cos(13.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(13 * π/12.0)]1000 [R2 * {square root over (ε_(x))} * cos(5.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(5 * π/12.0)] 1001 [R2 * {square root over(ε_(x))} * cos(19.0 * π/12.0), R2 * {square root over (ε_(x))} *sin(19 * π/12.0)] 1010 [R2 * {square root over (ε_(x))} * cos(7.0 *π/12.0), R2 * {square root over (ε_(x))} * sin(7 * π/12.0)] 1011 [R2 *{square root over (ε_(x))} * cos(17.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(17 * π/12.0)] 1100 [R1 * {square root over (ε_(x))} *cos(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 1101 [R1 *{square root over (ε_(x))} * cos(7.0 * π/4.0), R1 * {square root over(ε_(x))} * sin(7.0 * π/4.0)] 1110 [R1 * {square root over (ε_(x))} *cos(3.0 * π/4.0), R1 * {square root over (ε_(x))} * sin(3.0 * π/4.0)]1111 [R1 * {square root over (ε_(x))} * cos(5.0 * π/4.0), R1 * {squareroot over (ε_(x))} * sin(5.0 * π/4.0)]

a 32-APSK constellation, of a 4+12+16 bit/ring format, having bitlabeling and x-y bit positioning according to the following table (whereR1 represents the radius of an inner ring, R2 represents the radius of amiddle ring and R3 represents the radius of an outer ring, and4*R1²+12*R2²+16*R3²=32): Bit Label [x, y] Coordinates 00000 [R2 *{square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00001 [R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00010[R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 00011 [R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00100[−R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00110[−R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 00111 [−R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 01000[R3 * {square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 01001 [R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 01010 [R3 *{square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * cos(π/4.0)] 01011 [0, −R3 * {square root over (ε_(x))} ]01100 [−R3 * {square root over (ε_(x))} * sin(π/4.0), R3 * {square rootover (ε_(x))} * sin(π/4.0)] 01101 [0, R3 * {square root over (ε_(x))} ]01110 [−R3 * {square root over (ε_(x))} * cos(π/8.0), −R3 * {square rootover (ε_(x))} * sin(π/8.0)] 01111 [−R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * sin(π/8.0)] 10000 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 10001 [R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10010 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over(ε_(x))} * sin(π/12.0)] 10011 [R1 * {square root over (ε_(x))} *sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)] 10100 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 10101 [−R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10110 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over(ε_(x))} * sin(π/12.0)] 10111 [−R1 * {square root over (ε_(x))} *sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)] 11000 [R3 *{square root over (ε_(x))}, 0] 11001 [R3 * {square root over (ε_(x))} *sin(π/4.0), R3 * {square root over (ε_(x))} * sin(π/4.0)] 11010 [R3 *{square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 11011 [R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 11100 [−R3 *{square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 11101 [−R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 11110 [−R3 *{square root over (ε_(x))}, 0] 11111 [−R3 * {square root over (ε_(x))} *sin(π/4.0), −R3 * {square root over (ε_(x))} * sin(π/4.0)]

a 32-APSK constellation, of a 4+12+16 bit/ring format, having bitlabeling and x-y bit positioning according to the following table (whereR1 represents the radius of an inner ring, R2 represents the radius of amiddle ring and R3 represents the radius of an outer ring, and4*R1²+12*R2²+16*R3²=32): Bit Label [x, y] Coordinates 00000 [−R3 *{square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 00001 [−R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 00010 [R3 *{square root over (ε_(x))} * sin(π/8.0), R3 * {square root over(ε_(x))} * cos(π/8.0)] 00011 [0, R3 * {square root over (ε_(x))} ] 00100[−R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00110[R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00111 [R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 01000[−R3 * {square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 01001 [−R3 * {square root over (ε_(x))}, 0] 01010[R3 * {square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 01011 [R3 * {square root over (ε_(x))} *cos(π/8.0), R3 * {square root over (ε_(x))} * sin(π/8.0)] 01100 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 01101 [−R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 01110 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 01111 [R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10000 [−R3 *{square root over (ε_(x))} * sin(π/8.0), −R3 * {square root over(ε_(x))} * cos(π/8.0)] 10001 [0, −R3 * {square root over (ε_(x))} ]10010 [R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 * {square rootover (ε_(x))} * sin(π/4.0)] 10011 [R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 10100 [−R2 *{square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 10101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 10110[R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 10111 [R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 11000[−R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 11001 [−R3 * {square root over (ε_(x))} *cos(π/8.0), −R3 * {square root over (ε_(x))} * sin(π/8.0)] 11010 [R3 *{square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 11011 [R3 * {square root over (ε_(x))}, 0] 11100[−R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {squareroot over (ε_(x))} * sin(π/12.0)] 11101 [−R1 * {square root over(ε_(x))} * sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)]11110 [R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 *{square root over (ε_(x))} * sin(π/12.0)] 11111 [R1 * {square root over(ε_(x))} * sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)].


22. An apparatus according to claim 17, wherein the apparatus is furthercaused to perform the following: encoding, prior to the LDPC encoding,the one or more blocks of information bits of the source signal based ona t-error Bose Chaudhuri Hocquenghem (BCH) code.
 23. An apparatusaccording to claim 22, wherein the apparatus is further caused toperform the following: interleaving the LDPC encoded signal.
 24. Anapparatus according to claim 23, wherein the apparatus is further causedto perform the following: modulating the interleaved signal according toa signal constellation that comprises a one of the following formats(where ε_(x) represents average energy per symbol), a QPSK (QuadraturePhase Shift Keying) constellation having bit labeling and x-y bitpositioning according to the following table: Bit Label [x, y]Coordinates 00 [{square root over (ε_(x))} * cos(π/4.0), {square rootover (ε_(x))} * sin(π/4.0)] 01 [{square root over (ε_(x))} * cos(7.0 *π/4.0), {square root over (ε_(x))} * sin(7.0 * π/4.0)] 10 [{square rootover (ε_(x))} * cos(3.0 * π/4.0), {square root over (ε_(x))} * sin(3.0 *π/4.0)] 11 [{square root over (ε_(x))} * cos(5.0 * π/4.0), {square rootover (ε_(x))} * sin(5.0 * π/4.0)]

an 8-PSK (Phase Shift Keying) constellation having bit labeling and x-ybit positioning according to the following table: Bit Label [x, y]Coordinates 000 [{square root over (ε_(x))} * cos(π/8.0), {square rootover (ε_(x))} * sin(π/8.0)] 001 [{square root over (ε_(x))} * cos(15.0 *π/8.0), {square root over (ε_(x))} * sin(15.0 * π/8.0)] 010 [{squareroot over (ε_(x))} * cos(7.0 * π/8.0), {square root over (ε_(x))} *sin(7.0 * π/8.0)] 011 [{square root over (ε_(x))} * cos(9.0 * π/8.0),{square root over (ε_(x))} * sin(9.0 * π/8.0)] 100 [{square root over(ε_(x))} * cos(3.0 * π/8.0), {square root over (ε_(x))} * sin(3.0 *π/8.0)] 101 [{square root over (ε_(x))} * cos(13.0 * π/8.0), {squareroot over (ε_(x))} * sin(13.0 * π/8.0)] 110 [{square root over(ε_(x))} * cos(5.0 * π/8.0), {square root over (ε_(x))} * sin(5.0 *π/8.0)] 111 [{square root over (ε_(x))} * cos(11.0 * π/8.0), {squareroot over (ε_(x))} * sin(11.0 * π/8.0)]

a 16-APSK (Amplitude Phase Shift Keying) constellation, of a 4+12bit/ring format, having bit labeling and x-y bit positioning accordingto the following table (where R1 represents the radius of an inner ringand R2 represents the radius of an outer ring, and 4*R1²+12*R2²=16): BitLabel [x, y] Coordinates 0000 [R2 * {square root over (ε_(x))} *cos(3.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(3.0 * π/12.0)]0001 [R2 * {square root over (ε_(x))} * cos(21.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(21 * π/12.0)] 0010 [R2 * {square root over(ε_(x))} * cos(9.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(9 *π/12.0)] 0011 [R2 * {square root over (ε_(x))} * cos(15.0 * π/12.0),R2 * {square root over (ε_(x))} * sin(15 * π/12.0)] 0100 [R2 * {squareroot over (ε_(x))} * cos(π/12.0), R2 * {square root over (ε_(x))} *sin(π/12.0)] 0101 [R2 * {square root over (ε_(x))} * cos(23.0 * π/12.0),R2 * {square root over (ε_(x))} * sin(23 * π/12.0)] 0110 [R2 * {squareroot over (ε_(x))} * cos(11.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(11 * π/12.0)] 0111 [R2 * {square root over (ε_(x))} *cos(13.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(13 * π/12.0)]1000 [R2 * {square root over (ε_(x))} * cos(5.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(5 * π/12.0)] 1001 [R2 * {square root over(ε_(x))} * cos(19.0 * π/12.0), R2 * {square root over (ε_(x))} *sin(19 * π/12.0)] 1010 [R2 * {square root over (ε_(x))} * cos(7.0 *π/12.0), R2 * {square root over (ε_(x))} * sin(7 * π/12.0)] 1011 [R2 *{square root over (ε_(x))} * cos(17.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(17 * π/12.0)] 1100 [R1 * {square root over (ε_(x))} *cos(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 1101 [R1 *{square root over (ε_(x))} * cos(7.0 * π/4.0), R1 * {square root over(ε_(x))} * sin(7.0 * π/4.0)] 1110 [R1 * {square root over (ε_(x))} *cos(3.0 * π/4.0), R1 * {square root over (ε_(x))} * sin(3.0 * π/4.0)]1111 [R1 * {square root over (ε_(x))} * cos(5.0 * π/4.0), R1 * {squareroot over (ε_(x))} * sin(5.0 * π/4.0)]

a 32-APSK constellation, of a 4+12+16 bit/ring format, having bitlabeling and x-y bit positioning according to the following table (whereR1 represents the radius of an inner ring, R2 represents the radius of amiddle ring and R3 represents the radius of an outer ring, and4*R1²+12*R2²+16*R3²=32): Bit Label [x, y] Coordinates 00000 [R2 *{square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00001 [R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00010[R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 00011 [R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00100[−R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00110[−R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 00111 [−R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 01000[R3 * {square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 01001 [R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 01010 [R3 *{square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 01011 [0, −R3 * {square root over (ε_(x))}] 01100[−R3 * {square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 01101 [0, R3 * {square root over (ε_(x))}] 01110[−R3 * {square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 01111 [−R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 10000 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 10001 [R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10010 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over(ε_(x))} * sin(π/12.0)] 10011 [R1 * {square root over (ε_(x))} *sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)] 10100 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 10101 [−R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10110 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over(ε_(x))} * sin(π/12.0)] 10111 [−R1 * {square root over (ε_(x))} *sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)] 11000 [R3 *{square root over (ε_(x))}, 0] 11001 [R3 * {square root over (ε_(x))} *sin(π/4.0), R3 * {square root over (ε_(x))} * sin(π/4.0)] 11010 [R3 *{square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 11011 [R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 11100 [−R3 *{square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 11101 [−R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 11110 [−R3 *√ε_(x), 0] 11111 [−R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 *{square root over (ε_(x))} * sin(π/4.0)]

a 32-APSK constellation, of a 4+12+16 bit/ring format, having bitlabeling and x-y bit positioning according to the following table (whereR1 represents the radius of an inner ring, R2 represents the radius of amiddle ring and R3 represents the radius of an outer ring, and4*R1²+12*R2²+16*R3²=32): Bit Label [x, y] Coordinates 00000 [−R3 *{square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 00001 [−R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 00010 [R3 *{square root over (ε_(x))} * sin(π/8.0), R3 * {square root over(ε_(x))} * cos(π/8.0)] 00011 [0, R3 * {square root over (ε_(x))}] 00100[−R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00110[R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00111 [R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 01000[−R3 * {square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 01001 [−R3 * {square root over (ε_(x))}, 0] 01010[R3 * {square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 01011 [R3 * {square root over (ε_(x))} *cos(π/8.0), R3 * {square root over (ε_(x))} * sin(π/8.0)] 01100 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 01101 [−R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 01110 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 01111 [R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10000 [−R3 *{square root over (ε_(x))} * sin(π/8.0), −R3 * {square root over(ε_(x))} * cos(π/8.0)] 10001 [0, −R3 * {square root over (ε_(x))}] 10010[R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 10011 [R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 10100 [−R2 *{square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 10101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 10110[R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 10111 [R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 11000[−R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 11001 [−R3 * {square root over (ε_(x))} *cos(π/8.0), −R3 * {square root over (ε_(x))} * sin(π/8.0)] 11010 [R3 *{square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 11011 [R3 * {square root over (ε_(x))}, 0] 11100[−R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {squareroot over (ε_(x))} * sin(π/12.0)] 11101 [−R1 * {square root over(ε_(x))} * sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)]11110 [R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 *{square root over (ε_(x))} * sin(π/12.0)] 11111 [R1 * {square root over(ε_(x))} * sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)].


25. An apparatus comprising: accessing, by a processor of a device,stored information representing a predetermined structured parity checkmatrix of a Low Density Parity Check (LDPC) code, wherein the storedinformation reflects a tabular format of rows and columns, wherein eachrow represents occurrences of one values within a respective column ofthe parity check matrix, and wherein the columns of the parity checkmatrix are derived according to a predetermined operation based on therespective rows of the stored tabular information; and encoding one ormore blocks of information bits of a source signal based on the LDPCcode to generate an LDPC encoded signal; wherein the LDPC encoding ofthe blocks of information bits (each block being of a size of k_(ldpc)information bits, and each resulting encoded block being of a size ofn_(ldpc) code bits including parity bits p_(i), i=0, 1, 2, . . . ,n_(ldpc)−k_(ldpc)−1), comprises: initializing parity bit accumulatorsa₀=a₁= . . . =a_(n) _(ldpc) _(−k) _(ldpc) ⁻¹=0; for a one of the blocksof information bits, divided into j sequential groups (each of a size ofM information bits), and for j=1, 2, 3, . . . k_(ldpc)/M: (1)accumulating a first information bit of a j^(th) group in certain of theparity bit accumulators reflected by accumulator addresses based on aj^(th) row of the stored tabular information; and (2) accumulating theremaining (M−1) information bits of the j^(th) group in certain of theparity bit accumulators reflected by accumulator addresses according to${\{ {x + {m\mspace{14mu}{mod}\mspace{14mu} M}} \} - {\{ {\frac{x + {m\mspace{14mu}{mod}\mspace{14mu} M}}{M} - \frac{x}{M}} \}*M}},$wherein the division within the second bracketed term reflects integerdivision, and x denotes an address of the parity bit accumulatorcorresponding to the first bit of the group; and after all of theinformation bits are accumulated, starting with M=1, sequentiallyperforming operations (with respect to the parity bit accumulators)according to the following (where the additions are in Galois Field (GF)2), $\begin{matrix}{a_{M} = {a_{M} \oplus p_{0}}} \\{a_{2M} = {a_{2M} \oplus a_{M}}} \\{a_{3M} = {a_{3M} \oplus a_{2M}}}\end{matrix}$ ⋮      ⋮     ⋮ $\begin{matrix}{a_{n_{ldpc} - k_{ldpc} - M} = {a_{n_{ldpc} - k_{ldpc} - M} \oplus}} & {a_{n_{ldpc} - k_{ldpc} - {2M}}\;}\end{matrix}$ ⋮          ⋮            ⋮a₁ = a₁ ⊕ a_(n_(ldpc) − k_(ldpc) − M) a_(M + 1) = a_(M + 1) ⊕ a₁a_(2M + 1) = a_(2M + 1) ⊕ a_(M + 1)    ⋮       ⋮      ⋮ $\begin{matrix}{a_{n_{ldpc} - k_{ldpc} - M + 1} = {a_{n_{ldpc} - k_{ldpc} - M + 1} \oplus}} & {a_{n_{ldpc} - k_{ldpc} - {2M} + 1}\;}\end{matrix}$ ⋮          ⋮            ⋮a₂ = a₂ ⊕ a_(n_(ldpc) − k_(ldpc) − M + 1) a_(M + 2) = a_(M + 2) ⊕ a₂a_(2M + 2) = a_(2M + 2) ⊕ a_(M + 2)    ⋮       ⋮      ⋮ $\begin{matrix}{a_{n_{ldpc} - k_{ldpc} - M + 2} = {a_{n_{ldpc} - k_{ldpc} - M + 2} \oplus}} & {a_{n_{ldpc} - k_{ldpc} - {2M} + 2}\;}\end{matrix}$ ⋮          ⋮            ⋮a₃ = a₃ ⊕ a_(n_(ldpc) − k_(ldpc) − M + 2) a_(M + 3) = a_(M + 3) ⊕ a₃a_(2M + 3) = a_(2M + 3) ⊕ a_(M + 3)    ⋮       ⋮      ⋮ $\begin{matrix}{a_{n_{ldpc} - k_{ldpc} - M + 3} = {a_{n_{ldpc} - k_{ldpc} - M + 3} \oplus}} & {a_{n_{ldpc} - k_{ldpc} - {2M} + 3}\;}\end{matrix}$ ⋮          ⋮            ⋮ $\begin{matrix}{a_{M - 1} = {a_{M - 1} \oplus a_{n_{ldpc} - k_{ldpc} - 2}}} \\{a_{{2M} - 1} = {a_{{2M} - 2} \oplus a_{M - 1}}} \\{a_{{3M} - 1} = {a_{{3M} - 1} \oplus a_{{2M} - 1}}}\end{matrix}$ ⋮      ⋮     ⋮ $\begin{matrix}{a_{n_{ldpc} - k_{ldpc} - 1} = {a_{n_{ldpc} - k_{ldpc} - 1} \oplus}} & {a_{n_{ldpc} - k_{ldpc} - M - 1}\;}\end{matrix}$ wherein the parity bits p_(i), i=0, 1, . . .(n_(ldpc)−k_(ldpc)−1) are respectively reflected by the resulting paritybit accumulators a_(i), i=0, 1, . . . (n_(ldpc)−k_(ldpc)−1); and whereinthe stored information representing the structured parity check matrixcomprises a one of the following Tables 25a through 25k, TABLE 25aAddress of Parity Bit Accumulators (Rate 9/10) 405 3342 3664 6278 121538 4579 4801 776 3102 3279 5298 135 1119 4225 6307 440 902 3893 5464139 3289 5101 5543 1016 1893 3076 5942 2253 2759 5611 6055 335 1122 32605610 436 2337 2781 4648 2027 2451 5009 5137 1165 2440 4331 6125 17041858 3986 5327 938 2077 3080 5007 1239 1668 4309 4524 1464 2825 36404979 1682 3716 4081 5851 2709 2976 5931 6213 3811 5917 6342 1558 38184076 2290 5606 5807 2080 2467 4655 465 2866 4971 873 1881 4624 1301 22705161 1637 2567 4787 1380 4475 5563 258 2769 3845 240 1228 3387 46 52586393 583 1652 4139 2983 4137 5095 601 3064 3299 1821 6025 6123 775 32435674 822 3142 4768 3068 3255 6474 1006 2795 4896 2791 2997 5909 25833167 6427 1395 4398 5579 608 2248 3277 2491 5104 5580 2437 4228 4444 246568 3849 253 3723 4093 242 3968 6360 700 964 4904 1470 4714 5146 8661382 3801 1107 3368 4559 1679 1981 6041 1868 5706 6063 1602 1894 5142289 2726 4941 1943 3179 6347 2186 4446 5537 1055 3361 5448 531 2627 44481467 3414 5117 1738 4095 4628 1254 4214 5078 2218 5681 5936 272 50856284 139 1218 6269 576 3127 4258 1122 3584 3844 1795 4712 6092 1071 37544913 728 1868 3004 586 2425 2573 1986 3826 5894 217 1148 4123 1136 32013286 1138 4906 5344 548 3705 6148 2510 3974 4654 1846 2949 5959 23744890 6009 1495 2556 4359 582 4226 4406 233 3425 3922 1017 3734 5431 23585105 6251 260 418 2567 1627 2737 5360 788 3492 5646 1561 2057 4812 21475844 6217 952 2938 5458 1468 1837 4577 234 5186 6359 372 2505 2680 112461 3311 1294 3488 6350 1377 2441 6280 841 2776 5751 295 2591 5086 16284822 5080 3920 5608 5788 641 3885 4916 1482 3689 5845 2930 3257 5936 7504659 4733 1864 2899 4301 1068 1963 5753 2214 4295 4650 1367 3170 43061519 4107 5104 289 4410 4959 1252 5166 6162 389 1624 4422 1420 1543 4360669 3321 3631 125 1396 3536 2955 5317 6367 561 2194 4127 2206 4179 6352794 3549 5771 2570 3692 4924 2001 3095 4990 2380 5638 6039 733 2805 36872704 3062 6013 187 2154 5745 861 1833 5750 1197 2312 4677 941 2008 4171994 4565 5542 2058 3148 5976 789 1130 5079 448 4531 4763 1082 3375 57423455 5065 5744 621 1691 4313 90 4103 5953 1592 3266 3800 3144 5789 6418270 2561 3650 668 2477 6348 2011 3060 4880 1490 3886 4777 122 2583 63482484 2643 5308 714 3867 4171 192 2798 3938 2420 4733 6067 647 1656 377685 6080 6232 1058 3109 4875 3035 3305 5118 1711 4216 6044 918 2044 4085458 2522 4675 1113 2240 6268 1686 2087 5113 2385 2773 6280 1405 32165737 2016 4555 4733 853 3414 4395 3344 5214 5751 306 1153 5579

TABLE 25b Address of Parity Bit Accumulators (Rate 8/9) 185 1982 50906885 2051 2208 6645 7139 463 930 3108 5287 267 4014 6164 6820 1118 16293252 5478 1939 2411 4705 6527 3131 3252 5283 6315 1376 4003 5928 68751744 2522 4828 5888 775 1312 4686 6012 1147 2917 5313 5516 1657 28523653 6751 2580 3234 5634 5767 2344 2721 4417 6418 179 3305 3726 7140 2653322 4581 6309 443 2495 4394 4866 437 1796 3762 4139 768 1957 3793 3966647 892 4421 5589 990 2583 2887 4756 1066 1924 3116 6195 1993 3020 53755699 2781 4456 6173 6700 1280 1782 3254 5823 1102 1476 3325 5079 7171636 5021 5053 718 1445 2691 5432 1965 3073 5711 6010 1941 2496 48026018 2517 3299 5556 6486 825 3944 5793 6425 666 2499 2522 4531 287 6193347 3816 964 1328 4743 5169 1157 2369 4523 7043 127 4266 4568 6180 3073640 4260 6893 292 4052 6794 7117 3713 4114 6485 7015 916 1840 4808 5220139 438 3527 4645 654 1723 3612 4033 47 4410 4716 7198 1432 3782 41266347 41 1835 4267 5105 228 4313 5213 6963 894 3161 4884 5093 1561 28143746 6634 1393 1792 5407 5863 685 1078 2679 3088 1529 1937 5427 57811056 3146 4779 6602 649 2204 2568 6951 2768 3151 5521 6676 2074 24845833 6967 2398 3331 4515 5561 1280 3728 5934 6182 2485 3373 6190 68151141 3276 4393 6389 104 3339 7107 656 3450 5083 1912 3649 7037 273 21196733 916 4161 4570 2206 4605 6266 2610 3601 5771 723 1363 3961 2300 27906200 4199 4441 6771 1495 2820 5471 936 1329 5098 1475 5488 6486 11853676 4992 2330 5321 6307 2004 2901 5853 3133 3465 5656 120 4787 5879 3841757 4790 701 2989 6954 193 3359 3727 1352 3685 4958 1982 2227 5529 18413055 6728 225 498 6919 2731 4716 6809 1503 2052 5524 1234 3886 5007 13414384 7124 434 868 6365 2928 5292 5711 2569 4525 7013 2659 3072 6131 541995 5083 202 4311 5089 2258 6221 6630 1715 4295 6096 2435 4296 4435 9003540 5913 1671 3425 5981 1627 2049 5389 1946 3883 4259 1194 3432 60181903 6028 7168 67 3683 6193 2604 3891 5706 216 4278 4516 908 2717 54972309 4658 6455 1338 4593 6133 2279 5039 6588 334 4056 5129 3244 54606040 685 5104 6933 1369 2978 5006 2318 4819 7028 639 809 3032 585 15472797 966 3231 6705 1573 3363 6546 2085 6713 7136 1171 3970 5141 249 27694607 1519 4336 4827 377 1688 5622 3204 4717 6716 576 1078 3713 4697 57657128 1933 5226 6382 708 1625 2782 3166 5564 6505 808 2529 5679 64 11073749 1971 3071 4053 2298 4369 6479 1255 3962 5119 2359 5902 6978 1693333 3750 739 3475 6479 2380 3302 6020 1153 2982 6933 108 3675 4989 16843397 4607 2468 3309 5749 1567 3494 5287 2695 5500 6779 1650 3987 5381952 3655 5634 931 4061 5859 1862 3208 5942 114 1175 4355 59 3906 64521337 4180 7050 1052 2851 5200 2014 3149 6787 662 2573 4810 2249 60256192 1868 2250 6544 702 5004 6942 488 4582 6161

TABLE 25c Address of Parity Bit Accumulators (Rate ⅚) 798 1195 3207 35565147 5412 7636 8021 181 3530 5203 5661 7617 8048 10135 10609 1462 18983635 3961 6209 6648 8552 9391 761 2127 2918 5450 7539 7636 9676 98091878 2332 5152 5494 7238 7765 9607 9727 181 3351 5105 5496 7409 77029598 10763 433 2788 3838 5588 5828 7800 8720 9731 488 2907 3472 63276569 8352 8930 10689 89 2842 5508 6026 7669 8121 10349 10699 1925 22314325 5010 6583 7643 8721 9846 1073 1231 3228 4187 5319 6420 7491 8521154 2531 4592 5601 7458 7695 10201 10581 479 881 2553 5231 5431 78478862 9787 391 818 3787 4243 5817 7830 8104 10055 97 588 2769 3729 59736278 8902 9993 2045 2185 4299 6169 6816 8287 8827 10767 507 1663 27293810 4901 5789 7930 9212 2496 2802 4651 5027 6717 7163 9596 10444 1592056 4328 4854 6630 8590 9452 10469 105 1425 3252 3895 5416 6726 92049691 518 2749 3784 4758 5853 6843 8190 10706 331 2785 4978 5396 71628264 9814 10120 418 2240 2800 4818 6481 7079 8751 10595 1066 2927 41305387 6921 8198 9866 10247 25 3567 3892 5833 6308 7967 8287 10482 54 6792617 4622 4734 6949 8644 9208 214 525 4266 4365 6258 6756 8899 9914 20302273 4200 4413 6808 6929 9081 10322 810 1196 3735 4282 6022 6390 88119881 869 3411 3871 5997 7129 8067 9328 10212 833 7114 8123 432 2458 41081764 7069 9592 4174 5900 7187 2292 5716 8280 2941 4153 5310 3285 39186052 794 3044 8493 1528 2043 4966 2117 9315 10277 1191 2175 6178 14695270 7449 1107 1504 6235 2293 4650 6746 839 4508 9493 1715 5088 89313454 4487 9120 2059 7336 9626 3162 4847 8433 3098 9173 9491 3195 631710336 1402 2396 7200 1190 4378 7312 3132 3499 10186 1505 1947 10088 13563312 9270 4853 7227 8577 1760 7218 9050 1124 1500 9030 1133 1501 84841277 2932 10769 369 6143 7263 2624 4740 8068 2270 5183 10587 1490 52785741 2996 5955 10051 2646 5143 7804 3515 5866 9203 2007 4063 7813 27846381 6663 1535 4845 8402 2345 6141 9480 7229 9659 10068 5821 8323 8658388 5608 7239 4440 5599 8039 3254 3863 10116 145 4960 9463 4161 65336951 854 7196 8816 4022 7710 10676 1111 2194 8266 627 3218 3319 18844623 8735 1904 6509 9830 898 1433 3632 788 3712 8292 1668 7197 9130 3304454 10156 244 9082 10160 2683 3844 4759 1266 1752 5956 781 5063 103341256 1626 4876 1758 7765 8001 980 3659 7851 4149 8190 10202 92 3468 5352825 5942 7041 3015 7100 10738 3478 5859 8168 3629 9571 9750 5503 68188354 3328 7496 10540 169 4810 9788 4408 5712 6625 1988 5507 9347 4615210 8677 263 4203 8549 4588 7551 9631 2122 2239 8785 6645 9519 106242312 4343 8735 2199 4041 7078 1817 7474 8339 2908 6305 9881 3070 907710184 1137 6336 9262 437 2562 7750 671 2647 6444 3094 5542 5834 24984042 7138 3933 8184 8378 769 2671 9268 425 3579 5432 4120 4369 8476 5463291 5723 2273 2530 7559 425 1494 5071 275 1890 9065 4492 5010 10023 1471404 5990 4047 9339 10134 5177 7388 9568 2151 7534 10210 191 2601 63671124 3094 9452 1405 7140 9375 3908 9782 10082 1902 4924 8442 1706 43236831 1786 3732 6867 7563 8939 10016 5784 8885 10703 6173 8155 10542 30114950 7607 3283 8830 10655 895 5348 8081 2444 6732 7821 750 6367 6530

TABLE 25d Address of Parity Bit Accumulators (Rate ⅘) 498 2356 3399 46315536 7415 9550 9825 11986 499 722 3381 4400 7825 8864 9980 10902 12000923 1278 3976 5353 6383 7233 9807 11841 12067 1027 1141 3080 3450 62706615 8936 10053 12197 241 641 2589 3938 5948 7939 8405 10918 12913 11401748 3891 3977 5929 6450 8852 11141 11465 389 720 2956 3508 5292 63907424 9013 11890 913 2029 3157 6116 6139 8615 9640 10504 12410 1169 23563348 5141 5417 8732 9775 10888 11893 2068 2926 4223 6046 7006 9224 965112316 12691 1872 2497 4581 6490 8352 8820 10713 10983 12827 883 13382907 3415 6435 7383 9426 9937 11822 2638 2906 5312 5413 8136 9226 1011712244 12602 223 2800 4527 5538 6773 9346 9604 11204 12275 277 2712 38925465 5996 7851 10705 11551 12726 2053 2383 4042 4524 6654 7155 9091 938111287 1645 2733 3773 4901 5829 8913 9297 11284 12363 596 1703 2826 46574790 7024 7407 10286 10768 1260 7640 10440 413 1758 7516 6709 6900 110711638 11242 12568 247 4966 8252 2125 3685 7002 252 10234 11279 17 19215116 2515 4974 7892 2470 8033 12635 8169 10285 10536 7131 7997 117311646 4100 6581 5489 8335 10367 4315 5206 7834 3661 8534 10114 4825 853711665 4735 7855 11729 3636 7050 12359 5855 11577 12216 3709 4041 119741302 4819 9598 3726 5951 12780 439 6839 12862 6107 6862 10014 329 34009601 4365 4963 6828 2659 10871 12147 2956 5165 12608 1292 3562 8246 16949213 10369 558 1639 7845 5331 8084 10216 4385 4729 6706 5253 5424 11744718 1662 8953 8672 9013 10984 3992 4522 9006 1971 3055 6477 6282 75429563 3542 10674 12427 2869 8558 8790 2382 7955 11422 2227 5687 109177260 10148 11466 866 2025 6459 807 8584 11291 3185 5589 8581 724 421310711 6951 7549 12599 2034 2386 10704 306 2866 11776 1115 7630 9974 2267681 10061 1262 8047 11342 2579 11466 11672 5616 5900 9675 214 525 101892502 4013 9398 4192 8827 11901 749 8020 11632 2689 10394 12856 45 333112206 1852 3988 10681 1080 8893 11333 2708 11688 12168 144 4672 102896772 7703 8784 562 733 7714 768 5510 9791 519 9482 10071 1462 5139 91181443 2000 4859 1636 3443 6279 2989 3370 5667 5155 6176 7256 2052 52617773 2950 8290 11050 5767 6931 7984 4358 6356 10596 2486 10860 129191421 3168 9846 5989 8551 10654 4504 4762 12565 4925 6522 10829 7308 850312839 2383 7034 7547 3957 9245 12567 3857 9346 12337 3692 6689 6950 30844828 7816 977 3692 6597 1538 7007 9577 623 8432 10784 6408 7355 10231946 9879 12496 7515 8521 10900 4040 8421 10792 3361 5178 6908 2236 873510552 3647 6779 9745 5516 6702 12914 272 11360 11827 1847 4653 12103 257344 9583 2454 11437 12443 2047 4203 6137 6285 10091 11506 3281 46569090 4289 8798 12488 1220 9341 10946 73 3759 7981 6859 8176 10167 17554703 5322 1434 10905 12144 2380 3454 8174 1259 11673 12041 408 485212932 3116 5666 7879 2986 8641 10037 1022 6055 11595 1604 5858 7579 18605406 12830 2547 5839 9415 454 2602 4342 2697 5238 9006

TABLE 25e Address of Parity Bit Accumulators (Rate ¾) 755 3136 3253 55418180 13010 14277 15226 464 989 2773 3063 5246 5711 7829 10703 687 21745068 6955 8933 9180 12238 12247 620 868 3613 7063 7491 9977 11659 122311121 3221 3985 7303 8598 9677 11994 15459 239 3514 3734 5618 7483 944313290 14309 624 1641 4395 4791 8232 8520 11653 13714 1764 3468 3630 68838179 10354 10666 12589 5441 6021 9211 10116 11365 12476 15587 16031 11913709 4945 5821 9932 13549 13712 15675 4312 4559 6892 9729 11121 1284714493 15725 2522 4963 7683 8080 10332 10545 13579 15279 2324 2660 465010336 12099 12402 14149 14535 6217 6529 9102 11077 11401 13051 1424716145 1900 4014 6973 9765 10139 13297 15029 15931 356 3856 4735 819710020 13408 13819 16041 589 3148 4079 5870 6141 9278 11221 11732 31625352 6442 7233 8287 11507 13756 15666 1600 8280 14758 8404 8921 132481796 8643 13329 3470 5959 10511 1771 2651 10918 5690 14326 14698 49697444 13930 3426 9264 13439 6079 7897 12750 731 5131 12199 4567 945315026 804 12393 12657 1363 2349 15827 2393 5056 11552 183 11487 15154 331989 15052 352 2157 14479 2459 2678 11725 7572 8993 11156 4590 1050110934 3970 6836 16007 6430 6525 9597 2015 12757 14985 1842 6677 769212934 14875 15425 1165 6320 9437 1205 6831 8927 3986 8773 15795 73108501 14143 5813 10378 10472 3293 12137 15600 750 6051 8898 7955 1359516006 947 6895 16179 1474 5536 11069 214 1979 5872 1373 1461 13091 811612210 15540 188 2677 6413 2785 6824 14251 2798 8431 12629 470 1655 38724471 6408 8522 8263 11449 16194 9329 9687 11535 21 6478 13326 2904 714111399 701 7076 11584 3166 5197 15397 5328 5731 7774 875 12344 15421 917713008 14984 3884 7246 14544 3334 6747 10089 4492 10028 13128 2463 1243114331 2429 11404 14714 4661 11689 15261 6515 12787 14813 3354 9539 98579146 12412 12863 585 4001 7578 2300 7776 13341 3839 4001 14733 7541 982715058 5177 10853 12062 4861 10697 11004 1976 4984 9453 1118 10773 139501800 2888 4942 5525 10278 13858 1141 8799 14032 5552 8722 11930 375510366 15563 3879 6873 9914 1236 10327 13474 10007 12774 15695 2178 904716151 6256 7420 11075 7780 12124 14020 5611 7207 15439 2529 4322 150872714 5217 9884 81 10799 11594 1845 7854 12328 2480 4360 8883 1107 699110377 3479 5761 14289 5639 8855 9053 1460 3703 11295 7710 12577 143754720 12673 14956 1176 12155 13882 2187 6857 12985 1622 5874 9437 9422765 14378 3492 5768 12701 6432 14722 14794 11046 13036 15948 2904 42117521 229 592 4897 1616 8035 11683 10569 13395 14431 4474 6712 1515813340 13920 15592 5030 13245 15131 1061 6169 6794 328 6771 12242 839810475 10827 535 5368 9184 1903 5121 11454 745 2003 14697 503 3281 114353200 8219 8491 8299 9504 11601 4128 8160 16124 2994 4032 9680

TABLE 25f Address of Parity Bit Accumulators (Rate ⅔) 1615 2039 820011116 12879 13266 14888 1056 2837 5958 7722 10531 13028 16131 321 41966772 8327 18370 21171 21440 2720 4996 7486 11437 15927 16234 21032 2504778 5126 9839 16614 18590 21299 36 10862 13201 15758 17702 20512 213104548 8263 11202 12249 14424 17146 20605 521 2272 5846 7080 11967 1564217973 1858 5497 5858 7892 13057 15657 19262 65 1964 3694 6305 7236 1292414509 648 3736 6461 10779 13755 17583 19163 4991 6081 9123 11807 1214418877 20967 667 1787 6412 8270 13080 15684 19871 7185 7366 14404 1701117561 19430 21050 2701 4406 9153 9479 15365 19423 21462 3942 7315 1093314239 17054 17558 19977 1427 5839 8022 10208 16873 16924 21529 60 64597405 9609 11824 16053 19264 1956 4737 6790 9007 12579 16313 19839 69498003 10138 12354 14675 17960 20107 3267 6813 10410 12761 14996 1515117838 975 1375 3246 6456 9683 9895 14572 496 4250 9354 10365 14249 1672419585 4187 5342 7802 10016 10840 13690 14811 954 9023 12299 15481 1730819923 20256 1554 2755 4407 4842 10638 16587 17877 1953 3616 8712 1220614211 16877 21233 1295 4174 4522 9604 12613 14892 17298 500 3106 533412580 12669 15443 18409 2283 8824 9896 13581 13889 20424 20765 1332116111 18888 6938 17206 19746 1784 4153 15066 9407 14334 18336 5350 694210093 3170 8370 11789 905 1308 8307 3052 5479 14093 1269 16063 194422686 4519 8777 1756 3659 11721 3002 11645 18023 8978 10622 20164 884611139 13721 3066 10762 13957 3464 11167 13550 16215 18615 18961 767615415 18065 5396 10017 18358 7850 16492 18269 3531 16286 18989 573911192 13524 1009 18408 18920 6625 13662 15264 3505 12215 20200 842612029 20522 8496 19529 20705 2218 6541 11495 2253 5667 20631 2320 573919782 2335 8137 9814 1688 9285 15288 1393 8162 12727 3355 11661 14163142 10231 20568 9158 12878 13257 14324 17954 19658 2483 4417 18250 66110219 14001 6896 10200 14537 8802 17982 20021 2787 9042 14255 3101 1318018975 1164 8420 16306 6500 9735 12804 11842 14862 19904 7598 8199 179104273 17028 20983 544 9997 17358 3136 19586 20591 1785 5171 9714 838814782 18328 32 6240 10995 865 5080 8797 624 11476 14648 2163 7348 13686101 3574 18935 7330 13508 14000 5743 7379 9514 1592 11437 17432 48936775 20933 762 2691 7070 3030 19170 20360 4299 7845 19138 1978 658912314 2757 11178 14780 4956 5881 21471 3392 7590 19773 15990 19435 202271888 5932 16298 4085 5882 12449 4813 16665 20934 5522 9375 18435 1046612470 16771 11805 16606 21277 856 5550 18431 1094 12130 15534 1454917123 19074 5076 13100 17343 10615 16455 20767 13544 15381 16991 382918367 21333 15456 15532 19920 6866 15766 18286 6461 8677 12234 202612038 20327 3839 8318 10649 4613 11022 15972 3757 13434 15910 4519 646111133

TABLE 25g Address of Parity Bit Accumulators (Rate ⅗) 487 2424 5103 629414728 16989 22394 22707 1634 5235 7897 8219 10473 10926 15226 17159 78368222 10026 12421 17812 20194 21551 25762 178 4183 5238 8916 11565 1351317234 23622 2619 3761 6539 10279 11943 16294 19745 22819 1097 3310 529710950 12939 13749 18284 19985 5062 8675 11402 13351 14655 16741 2055322461 5862 7897 12406 13503 16929 17631 20389 22142 1160 8004 9813 1354014666 18003 22246 24879 157 6179 13015 16673 17089 19482 23223 243241568 3396 5983 13072 13336 18349 18521 21010 3632 5935 7011 12522 1585717935 18950 23596 7555 8375 10646 12391 15071 20478 22501 23402 20002378 7387 11854 13513 21598 24971 25503 476 2578 7339 8402 13753 1614719513 22512 1646 7593 8714 9846 12535 14403 21897 22723 913 3205 53846134 13821 16335 23236 24236 502 1494 5665 8092 9094 13273 18152 238563571 5849 7970 10318 16538 19009 19186 24775 1768 5020 10749 15104 1844621191 21392 25505 279 7272 9982 10336 13151 15451 18316 22103 2005 40264677 7991 9235 13384 14754 23731 1319 3499 6567 7679 11063 15094 1526717449 6162 6797 10759 11683 12866 13911 17226 22718 2382 9187 1180816423 18162 19122 21873 22911 216 1114 7075 14485 16966 19607 2291424691 721 2693 6387 8821 17550 19330 22719 24673 972 2842 8828 993312899 15009 15268 23746 1947 4539 10078 12725 13876 18387 20589 247831755 4300 6903 8799 14179 14485 20595 24429 3854 4896 7018 10751 1401614346 16861 19163 3859 4085 5919 7733 15182 16468 19409 21431 1371 676310705 10999 14233 17684 21160 22018 2356 5185 5651 12200 12308 1638418868 21030 6600 8655 9801 11712 13854 16725 20795 25380 1692 3627 69627462 10218 21056 21314 24003 16314 19603 22678 1179 19957 21941 1416319047 24512 10474 20933 24258 461 8308 11535 7361 11441 12375 40 641710855 6001 22526 23757 1071 3964 9467 2756 6525 23536 449 3246 1178212053 19545 21812 2670 3701 10363 7809 17817 20062 2900 6138 24663 70429061 22324 7149 12133 15790 7464 15848 22261 4406 15275 21965 2305 824015658 844 3405 18366 1893 2451 17338 5810 17934 20992 2244 4845 2415817878 18964 23878 5429 22314 24712 303 14398 24478 15836 18743 218264587 17442 23891 9067 19984 25568 12659 20803 25727 5409 6673 23824 969215061 18694 861 1169 16870 12226 14993 20284 13054 14784 20185 160 1550123163 614 18992 23847 4719 15363 20481 19129 23171 24212 5465 2165025118 3669 15823 17361 12767 13112 21339 4658 14270 17975 503 1129614239 16728 20243 25123 1952 12991 19964 11201 17284 18410 2840 1287724940 4989 21344 23127 3268 15681 23795 2050 16692 25423 4144 9210 10293896 8604 15852 9235 23106 25062 4425 5548 25280 4343 10845 11308 32249603 25270 1859 10301 21895 4944 11025 23373 5530 9419 25244 8525 1589618435 8591 19838 24964 18261 19436 25885 4301 15776 15875 9532 1615820694 9674 11995 20018 8382 9360 12086 2974 19579 25776 2968 4956 207853009 11349 25614 2975 11230 25789

TABLE 25h Address of Parity Bit Accumulators (Rate ½) 1690 4392 724310123 12751 19068 23261 25882 25950 4295 8310 13735 14903 18216 1852120457 22873 26999 2900 6292 14253 16327 19561 21463 23348 26738 311081201 2187 4037 6084 7112 17403 20499 23973 29486 1913 5146 8684 1076211063 15735 19611 22881 27218 1569 1918 5946 8361 9717 12102 16573 1918728309 925 7530 10304 16459 18002 20820 22693 24097 30913 4336 1431516734 16940 19494 19977 21895 25121 31768 3367 3872 10516 11797 1608018647 21646 24129 31143 1557 4179 6997 9985 19179 23292 24350 2683428821 2605 4611 6484 13227 16750 22762 26200 28877 31731 3139 6378 79439983 10171 14917 17887 19560 25630 5706 5916 8409 10080 13664 1375320142 22989 29228 4479 7229 10272 12943 17716 21870 24521 29638 32330818 2084 5177 9571 10713 14061 27997 28946 31914 4223 8466 15465 1624118591 20686 25672 28312 31533 3049 3335 8311 11572 17578 22419 2372427334 27454 607 4010 11542 13746 16393 19392 21126 28048 28409 1687 20904816 6641 7824 8909 10871 25465 30399 1282 3011 6333 8010 10952 1695824124 26242 32302 2156 4900 6829 9255 15769 16823 25927 30541 30839 31335074 7609 10078 13090 15951 22294 27409 28021 588 1624 7313 9206 1290815670 21180 22034 30955 3342 7385 7790 11060 13010 17437 21755 2805228308 3431 5338 15158 18950 23091 24334 26495 28510 30791 515 3366 1186015866 18097 19816 20516 23868 32139 219 6739 12840 20551 23331 2353025670 28997 32168 152 1161 11055 18106 18657 20617 25241 26437 306924846 9453 14029 14862 20321 22192 26263 26518 29656 3613 6463 1222915428 17644 19554 20150 27965 31614 110 6876 9265 14936 18681 31853 366116313 30499 271 6718 20110 21531 29984 30553 1164 17609 23628 8154 1338224492 3653 10000 31610 2337 21448 28080 11999 15213 25875 12821 3128631518 6097 17194 24909 9702 24304 28525 5883 18252 26861 16032 1783420825 8986 16741 21021 568 27281 27400 13853 15558 19265 1005 5259 1224310050 23589 27597 758 7779 12074 2783 12248 14536 810 1354 27229 636220993 27191 10553 18772 30110 2402 2835 21129 12261 15601 22445 1144215365 22496 9669 16977 21706 5711 13362 23591 17344 21970 29298 24013300 29750 12151 27394 32351 2346 25180 25427 2473 16162 20178 37727888 29067 4813 22325 26724 5566 11255 14096 11274 26442 28451 573314961 21477 9204 11769 32017 4994 8043 9090 5419 10606 24702 7182 1124314543 13457 24507 29332 7082 21960 26549 13422 17659 31308 4351 3002630998 11180 13085 17157 18933 21543 23781 14066 18961 22375 8255 1238819309 2529 12598 29636 8811 28673 31573 8938 24504 30413 14629 2490630234 14478 24007 30182 2559 14678 29540 25088 25451 28782 553 2550729461

TABLE 25i Address of Parity Bit Accumulators (Rate ⅖) 4173 6386 681315139 16380 22095 22454 24964 26820 27326 30289 32188 826 1264 3864 77789667 17876 20474 21361 24378 24599 28142 33137 229 1256 4395 6290 666415376 17436 19340 19463 28818 33008 36039 3801 8483 10585 12292 1341814753 17085 18901 21746 22945 35570 37330 1056 7871 8934 9916 1213117573 20277 23395 30197 33313 35985 37827 367 6393 7261 12313 1695618789 19865 22650 23639 24535 31056 36744 4276 10788 13433 16512 1738420031 26177 27799 29564 30931 33354 37567 1446 3707 5576 7649 9769 1172315461 19981 23591 30056 34358 36599 4336 4879 6768 8836 11153 1616318737 26233 28194 29209 32440 36228 4993 6006 9212 11740 14173 1652624459 25254 29745 33408 36055 36434 664 2361 9581 15385 18970 2068322481 25313 25573 28771 29109 38646 60 4096 7203 9634 13663 17240 2206922446 25032 35038 36150 37117 531 2834 6551 13051 17419 18553 2146423928 26936 29707 32040 37070 1518 2753 6081 6875 9167 10435 12956 2011723116 24850 32134 38490 3408 7120 7440 10653 12980 16264 21753 2801029934 31090 32798 37138 1625 2003 12165 12307 18588 19634 22220 2404724332 32481 32815 36389 43 5869 9888 13215 14897 16193 17231 19751 2840334240 37503 37977 995 8360 11257 11794 14564 20565 24887 27011 2937231511 36783 37169 1807 2320 5317 5423 14505 18577 20893 27636 3086533909 37026 38577 2917 3575 8016 11563 15569 17766 20889 24069 2434135063 38343 38694 127 2839 6382 9940 11027 12217 14285 27540 27894 3119931358 34474 1933 4300 6891 13497 16865 20989 22027 28776 29073 3224833905 38280 1378 3266 8115 10258 14509 21738 25522 25610 28824 2936231876 33896 849 7607 10285 10474 12436 16182 19495 21673 29264 3270635784 38261 18317 32445 34841 3016 3492 27531 11220 27356 31589 1421319144 37905 17819 20378 21592 25822 27680 28748 11051 18497 31183 875922683 30156 8604 15941 32844 19298 23156 30575 21482 28103 37945 21425436 35950 2977 10390 20959 1436 7104 12063 14316 22841 36453 4795 1510725769 4674 5422 31791 3026 11082 34646 13803 18011 35474 22733 3361734598 2430 11376 17648 19089 27031 33569 3748 31787 38672 1716 2854130394 18278 33786 34836 8313 26157 32033 2619 34491 37580 31387 3383435739 5034 11365 26172 24580 30460 33982 4375 14974 34935 6085 815925482 12728 23556 35511 2361 35221 35496 7948 15663 37449 12946 1302623162 9367 13954 16799 15553 18209 29641 9304 24815 26869 5095 2663930677 14012 20605 23633 12915 13984 30821 9349 16778 23849 16874 2654126754 15642 20257 28066 7505 14992 20745 547 5328 26296 5178 8851 26552

TABLE 25j Address of Parity Bit Accumulators (Rate ⅓) 7127 12217 1490317792 19690 23709 26904 31847 32174 37971 39934 43192 631 3892 3961 71109168 14664 20881 33763 34077 38290 38589 40587 1561 4952 12735 1705017363 23114 23432 26431 30725 34201 38679 41775 3120 6362 9346 1020219293 21581 26158 28110 28791 30854 37723 39609 937 3213 3271 8272 903515349 18735 23617 27626 33046 35819 42715 42 5281 15192 15731 2068723236 29529 31564 32442 35605 36703 42323 3415 5078 7595 8830 1629816735 18395 18860 20659 21190 24417 39339 1247 3506 4592 7574 1179914188 22214 27862 31190 33446 39010 39447 659 6732 8711 10845 1496720932 21392 24561 27950 30282 34491 39662 1574 6084 6401 10616 1549621480 22587 24801 28997 34755 40468 40765 1816 5243 8287 9380 1279513208 22838 23280 31453 35837 36957 38620 2526 5720 11010 12022 1520019448 27202 27673 29334 32919 36071 42350 542 3767 8589 14736 1759918679 20408 29296 37332 38338 40657 42203 1274 6050 11401 13088 1427117551 31621 32620 36895 37191 39291 43194 312 4625 6259 6839 10672 1669521781 27493 27928 31056 33505 41398 167 1811 6813 10155 10651 1554416043 23824 28470 32607 35112 37845 2477 2675 8067 19670 22707 2706929018 30917 33456 37625 40865 42750 2232 8590 13476 14000 16942 2302623964 26975 29689 33460 36770 41758 2199 4775 7747 8795 17270 1886621982 24102 29704 34123 34954 41148 2130 4709 11954 12300 19938 2529925579 28797 30414 36228 36617 42694 1336 22318 25169 18630 24904 2607119828 24680 29215 33916 41065 41539 14761 30074 40827 10013 20112 2593214530 21735 41427 12985 26680 37635 7003 9909 14113 16556 18312 2060618051 19132 21794 4506 10959 16641 13543 16372 29889 9717 22665 3732430086 36117 40152 19395 33829 38170 3120 17782 40104 1599 30981 352935514 10349 25365 5646 10000 25213 5839 12560 41786 20495 31791 347104251 31730 33042 1029 12241 28921 4009 32368 35306 7216 13773 3649512623 22397 34316 20441 24199 41893 15962 17883 25624 13355 13717 3566724883 27266 28103 24291 28357 34576 964 35256 39973 11315 18036 391202832 16014 25615 3789 7400 11418 9383 32137 37908 11721 30386 39012 796326523 43088 7442 11584 26585

TABLE 25k Address of Parity Bit Accumulators (Rate ¼) 4154 7271 1860826981 29145 30753 34895 36931 37422 42768 47366 47722 3011 5069 61569587 12589 20148 33306 36809 37089 44032 45205 48468 39 1332 8129 1965021273 25443 26292 28737 31676 33999 34500 38260 2180 2761 8052 1075016919 18907 23210 24269 26621 34815 39889 43751 1473 1960 13924 2141023195 27618 32955 36079 38702 41888 44387 44654 4943 6550 9829 1489315444 19815 24320 29734 33955 36141 42602 45015 1132 3914 6903 1215412305 16298 20487 25855 29304 32150 39228 47188 880 8771 13199 1596521881 22783 25410 28163 31814 34217 38887 40142 2890 7245 11208 1876121093 26680 31955 38349 40180 43274 43710 46286 296 571 2760 9305 1352914589 17815 28360 30693 33015 35716 39781 3678 9475 12627 13894 1626719135 22641 24756 28788 33357 35290 46414 2066 9907 11657 15142 1551621000 22945 27012 29663 40795 44925 47884 713 4869 6526 10360 1492021797 31226 35575 41795 42905 45382 45984 1015 4061 6411 8415 1149413574 23760 24879 27137 37539 42259 45488 8455 11853 14155 16832 1931819778 27886 28893 36425 41079 43947 48266 5393 17152 43557 17300 2504448036 25767 28037 31468 4322 42152 44324 27676 46770 47870 23456 2479130363 7899 10123 45744 7716 12923 33714 18718 30285 40475 1794 1803532276 26277 33598 38109 8757 21965 40705 7007 12090 17815 17010 2201037440 3493 13085 32557 10988 18098 20180 2166 11137 23546 15518 2055035071 26272 41471 46610 4430 14274 35788 23839 29219 43155 17336 2077032566 10570 16186 35139 5836 22534 38783 5863 36391 41378 5580 3097141722 5558 30075 39521 14465 39539 40407 3369 30151 46801 9211
 3788046862.


26. An apparatus according to claim 25, wherein row indices of 1's in acolumn index j*M (j=0, 1, 2, 3, . . . , k_(ldpc)/M−1) of the paritycheck matrix are given at the j^(th) row according to the one Table. 27.An apparatus according to claim 25, wherein the LDPC code is of astructure that facilitates use of a plurality of parallel engines fordecoding the encoded signal.
 28. An apparatus according to claim 25,wherein the apparatus is further caused to perform the following:modulating the LDPC coded signal according to a signal constellationreflecting one of QPSK (Quadrature Phase Shift Keying), OQPSK (OffsetQPSK), PSK (Phase Shift Keying), 8-PSK, 16-APSK (Amplitude PSK), and32-APSK.
 29. An apparatus according to claim 25, wherein the apparatusis further caused to perform the following: modulating the encodedsignal according to a signal constellation that comprises a one of thefollowing formats (where ε_(x) represents average energy per symbol), aQPSK (Quadrature Phase Shift Keying) constellation having bit labelingand x-y bit positioning according to the following table: Bit Label [x,y] Coordinates 00 [{square root over (ε_(x))} * cos(π/4.0), {square rootover (ε_(x))} * sin(π/4.0)] 01 [{square root over (ε_(x))} * cos(7.0 *π/4.0), {square root over (ε_(x))} * sin(7.0 * π/4.0)] 10 [{square rootover (ε_(x))} * cos(3.0 * π/4.0), {square root over (ε_(x))} * sin(3.0 *π/4.0)] 11 [{square root over (ε_(x))} * cos(5.0 * π/4.0), {square rootover (ε_(x))} * sin(5.0 * π/4.0)]

an 8-PSK (Phase Shift Keying) constellation having bit labeling and x-ybit positioning according to the following table: Bit Label [x, y]Coordinates 000 [{square root over (ε_(x))} * cos(π/8.0), {square rootover (ε_(x))} * sin(π/8.0)] 001 [{square root over (ε_(x))} * cos(15.0 *π/8.0), {square root over (ε_(x))} * sin(15.0 * π/8.0)] 010 [{squareroot over (ε_(x))} * cos(7.0 * π/8.0), {square root over (ε_(x))} *sin(7.0 * π/8.0)] 011 [{square root over (ε_(x))} * cos(9.0 * π/8.0),{square root over (ε_(x))} * sin(9.0 * π/8.0)] 100 [{square root over(ε_(x))} * cos(3.0 * π/8.0), {square root over (ε_(x))} * sin(3.0 *π/8.0)] 101 [{square root over (ε_(x))} * cos(13.0 * π/8.0), {squareroot over (ε_(x))} * sin(13.0 * π/8.0)] 110 [{square root over(ε_(x))} * cos(5.0 * π/8.0), {square root over (ε_(x))} * sin(5.0 *π/8.0)] 111 [{square root over (ε_(x))} * cos(11.0 * π/8.0), {squareroot over (ε_(x))} * sin(11.0 * π/8.0)]

a 16-APSK (Amplitude Phase Shift Keying) constellation, of a 4+12bit/ring format, having bit labeling and x-y bit positioning accordingto the following table (where R1 represents the radius of an inner ringand R2 represents the radius of an outer ring, and 4*R1²+12*R2²=16): BitLabel [x, y] Coordinates 0000 [R2 * {square root over (ε_(x))} *cos(3.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(3.0 * π/12.0)]0001 [R2 * {square root over (ε_(x))} * cos(21.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(21 * π/12.0)] 0010 [R2 * {square root over(ε_(x))} * cos(9.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(9 *π/12.0)] 0011 [R2 * {square root over (ε_(x))} * cos(15.0 * π/12.0),R2 * {square root over (ε_(x))} * sin(15 * π/12.0)] 0100 [R2 * {squareroot over (ε_(x))} * cos(π/12.0), R2 * {square root over (ε_(x))} *sin(π/12.0)] 0101 [R2 * {square root over (ε_(x))} * cos(23.0 * π/12.0),R2 * {square root over (ε_(x))} * sin(23 * π/12.0)] 0110 [R2 * {squareroot over (ε_(x))} * cos(11.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(11 * π/12.0)] 0111 [R2 * {square root over (ε_(x))} *cos(13.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(13 * π/12.0)]1000 [R2 * {square root over (ε_(x))} * cos(5.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(5 * π/12.0)] 1001 [R2 * {square root over(ε_(x))} * cos(19.0 * π/12.0), R2 * {square root over (ε_(x))} *sin(19 * π/12.0)] 1010 [R2 * {square root over (ε_(x))} * cos(7.0 *π/12.0), R2 * {square root over (ε_(x))} * sin(7 * π/12.0)] 1011 [R2 *{square root over (ε_(x))} * cos(17.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(17 * π/12.0)] 1100 [R1 * {square root over (ε_(x))} *cos(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 1101 [R1 *{square root over (ε_(x))} * cos(7.0 * π/4.0), R1 * {square root over(ε_(x))} * sin(7.0 * π/4.0)] 1110 [R1 * {square root over (ε_(x))} *cos(3.0 * π/4.0), R1 * {square root over (ε_(x))} * sin(3.0 * π/4.0)]1111 [R1 * {square root over (ε_(x))} * cos(5.0 * π/4.0), R1 * {squareroot over (ε_(x))} * sin(5.0 * π/4.0)]

a 32-APSK constellation, of a 4+12+16 bit/ring format, having bitlabeling and x-y bit positioning according to the following table (whereR1 represents the radius of an inner ring, R2 represents the radius of amiddle ring and R3 represents the radius of an outer ring, and4*R1²+12*R2²+16*R3²=32): Bit Label [x, y] Coordinates 00000 [R2 *{square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00001 [R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00010[R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 00011 [R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00100[−R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00110[−R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 00111 [−R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 01000[R3 * {square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 01001 [R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 01010 [R3 *{square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 01011 [0, −R3 * {square root over (ε_(x))}] 01100[−R3 * {square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 01101 [0, R3 * {square root over (ε_(x))}] 01110[−R3 * {square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 01111 [−R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 10000 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 10001 [R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10010 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over(ε_(x))} * sin(π/12.0)] 10011 [R1 * {square root over (ε_(x))} *sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)] 10100 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 10101 [−R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10110 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over(ε_(x))} * sin(π/12.0)] 10111 [−R1 * {square root over (ε_(x))} *sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)] 11000 [R3 *{square root over (ε_(x))}, 0] 11001 [R3 * {square root over (ε_(x))} *sin(π/4.0), R3 * {square root over (ε_(x))} * sin(π/4.0)] 11010 [R3 *{square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 11011 [R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 11100 [−R3 *{square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 11101 [−R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 11110 [−R3 *{square root over (ε_(x))}, 0] 11111 [−R3 * {square root over (ε_(x))} *sin(π/4.0), −R3 * {square root over (ε_(x))} * sin(π/4.0)]

a 32-APSK constellation, of a 4+12+16 bit/ring format, having bitlabeling and x-y bit positioning according to the following table (whereR1 represents the radius of an inner ring, R2 represents the radius of amiddle ring and R3 represents the radius of an outer ring, and4*R1²+12*R2²+16*R3²=32): Bit Label [x, y] Coordinates 00000 [−R3 *{square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 00001 [−R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 00010 [R3 *{square root over (ε_(x))} * sin(π/8.0), R3 * {square root over(ε_(x))} * cos(π/8.0)] 00011 [0, R3 * {square root over (ε_(x))}] 00100[−R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00110[R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00111 [R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 01000[−R3 * {square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 01001 [−R3 * {square root over (ε_(x))}, 0] 01010[R3 * {square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 01011 [R3 * {square root over (ε_(x))} *cos(π/8.0), R3 * {square root over (ε_(x))} * sin(π/8.0)] 01100 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 01101 [−R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 01110 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 01111 [R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10000 [−R3 *{square root over (ε_(x))} * sin(π/8.0), −R3 * {square root over(ε_(x))} * cos(π/8.0)] 10001 [0, −R3 * {square root over (ε_(x))}] 10010[R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 10011 [R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 10100 [−R2 *{square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 10101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 10110[R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 10111 [R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 11000[−R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 11001 [−R3 * {square root over (ε_(x))} *cos(π/8.0), −R3 * {square root over (ε_(x))} * sin(π/8.0)] 11010 [R3 *{square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 11011 [R3 * {square root over (ε_(x))}, 0] 11100[−R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {squareroot over (ε_(x))} * sin(π/12.0)] 11101 [−R1 * {square root over(ε_(x))} * sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)]11110 [R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 *{square root over (ε_(x))} * sin(π/12.0)] 11111 [R1 * {square root over(ε_(x))} * sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)].


30. An apparatus according to claim 25, wherein the apparatus is furthercaused to perform the following: encoding, prior to the LDPC encoding,the one or more blocks of information bits of the source signal based ona t-error Bose Chaudhuri Hocquenghem (BCH) code.
 31. An apparatusaccording to claim 30, wherein the apparatus is further caused toperform the following: interleaving the LDPC encoded signal.
 32. Anapparatus according to claim 31, wherein the apparatus is further causedto perform the following: modulating the interleaved signal according toa signal constellation that comprises a one of the following formats(where ε_(x) represents average energy per symbol), a QPSK (QuadraturePhase Shift Keying) constellation having bit labeling and x-y bitpositioning according to the following table: Bit Label [x, y]Coordinates 00 [{square root over (ε_(x))} * cos(π/4.0), {square rootover (ε_(x))} * sin(π/4.0)] 01 [{square root over (ε_(x))} * cos(7.0 *π/4.0), {square root over (ε_(x))} * sin(7.0 * π/4.0)] 10 [{square rootover (ε_(x))} * cos(3.0 * π/4.0), {square root over (ε_(x))} * sin(3.0 *π/4.0)] 11 [{square root over (ε_(x))} * cos(5.0 * π/4.0), {square rootover (ε_(x))} * sin(5.0 * π/4.0)]

an 8-PSK (Phase Shift Keying) constellation having bit labeling and x-ybit positioning according to the following table: Bit Label [x, y]Coordinates 000 [{square root over (ε_(x))} * cos(π/8.0), {square rootover (ε_(x))} * sin(π/8.0)] 001 [{square root over (ε_(x))} * cos(15.0 *π/8.0), {square root over (ε_(x))} * sin(15.0 * π/8.0)] 010 [{squareroot over (ε_(x))} * cos(7.0 * π/8.0), {square root over (ε_(x))} *sin(7.0 * π/8.0)] 011 [{square root over (ε_(x))} * cos(9.0 * π/8.0),{square root over (ε_(x))} * sin(9.0 * π/8.0)] 100 [{square root over(ε_(x))} * cos(3.0 * π/8.0), {square root over (ε_(x))} * sin(3.0 *π/8.0)] 101 [{square root over (ε_(x))} * cos(13.0 * π/8.0), {squareroot over (ε_(x))} * sin(13.0 * π/8.0)] 110 [{square root over(ε_(x))} * cos(5.0 * π/8.0), {square root over (ε_(x))} * sin(5.0 *π/8.0)] 111 [{square root over (ε_(x))} * cos(11.0 * π/8.0), {squareroot over (ε_(x))} * sin(11.0 * π/8.0)]

a 16-APSK (Amplitude Phase Shift Keying) constellation, of a 4+12bit/ring format, having bit labeling and x-y bit positioning accordingto the following table (where R1 represents the radius of an inner ringand R2 represents the radius of an outer ring, and 4*R1²+12*R2²=16): BitLabel [x, y] Coordinates 0000 [R2 * {square root over (ε_(x))} *cos(3.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(3.0 * π/12.0)]0001 [R2 * {square root over (ε_(x))} * cos(21.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(21 * π/12.0)] 0010 [R2 * {square root over(ε_(x))} * cos(9.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(9 *π/12.0)] 0011 [R2 * {square root over (ε_(x))} * cos(15.0 * π/12.0),R2 * {square root over (ε_(x))} * sin(15 * π/12.0)] 0100 [R2 * {squareroot over (ε_(x))} * cos(π/12.0), R2 * {square root over (ε_(x))} *sin(π/12.0)] 0101 [R2 * {square root over (ε_(x))} * cos(23.0 * π/12.0),R2 * {square root over (ε_(x))} * sin(23 * π/12.0)] 0110 [R2 * {squareroot over (ε_(x))} * cos(11.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(11 * π/12.0)] 0111 [R2 * {square root over (ε_(x))} *cos(13.0 * π/12.0), R2 * {square root over (ε_(x))} * sin(13 * π/12.0)]1000 [R2 * {square root over (ε_(x))} * cos(5.0 * π/12.0), R2 * {squareroot over (ε_(x))} * sin(5 * π/12.0)] 1001 [R2 * {square root over(ε_(x))} * cos(19.0 * π/12.0), R2 * {square root over (ε_(x))} *sin(19 * π/12.0)] 1010 [R2 * {square root over (ε_(x))} * cos(7.0 *π/12.0), R2 * {square root over (ε_(x))} * sin(7 * π/12.0)] 1011 [R2 *{square root over (ε_(x))} * cos(17.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(17 * π/12.0)] 1100 [R1 * {square root over (ε_(x))} *cos(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 1101 [R1 *{square root over (ε_(x))} * cos(7.0 * π/4.0), R1 * {square root over(ε_(x))} * sin(7.0 * π/4.0)] 1110 [R1 * {square root over (ε_(x))} *cos(3.0 * π/4.0), R1 * {square root over (ε_(x))} * sin(3.0 * π/4.0)]1111 [R1 * {square root over (ε_(x))} * cos(5.0 * π/4.0), R1 * {squareroot over (ε_(x))} * sin(5.0 * π/4.0)]

a 32-APSK constellation, of a 4+12+16 bit/ring format, having bitlabeling and x-y bit positioning according to the following table (whereR1 represents the radius of an inner ring, R2 represents the radius of amiddle ring and R3 represents the radius of an outer ring, and4*R1²+12*R2²+16*R3²=32): Bit Label [x, y] Coordinates 00000 [R2 *{square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00001 [R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00010[R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 00011 [R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00100[−R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00110[−R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 00111 [−R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 01000[R3 * {square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 01001 [R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 01010 [R3 *{square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 01011 [0, −R3 * {square root over (ε_(x))}] 01100[−R3 * {square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 01101 [0, R3 * {square root over (ε_(x))}] 01110[−R3 * {square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 01111 [−R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 10000 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 10001 [R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10010 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over(ε_(x))} * sin(π/12.0)] 10011 [R1 * {square root over (ε_(x))} *sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)] 10100 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 10101 [−R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10110 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {square root over(ε_(x))} * sin(π/12.0)] 10111 [−R1 * {square root over (ε_(x))} *sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)] 11000 [R3 *{square root over (ε_(x))}, 0] 11001 [R3 * {square root over (ε_(x))} *sin(π/4.0), R3 * {square root over (ε_(x))} * sin(π/4.0)] 11010 [R3 *{square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 11011 [R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 11100 [−R3 *{square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 11101 [−R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 11110 [−R3 *{square root over (ε_(x))}, 0] 11111 [−R3 * {square root over (ε_(x))} *sin(π/4.0), −R3 * {square root over (ε_(x))} * sin(π/4.0)]

a 32-APSK constellation, of a 4+12+16 bit/ring format, having bitlabeling and x-y bit positioning according to the following table (whereR1 represents the radius of an inner ring, R2 represents the radius of amiddle ring and R3 represents the radius of an outer ring, and4*R1²+12*R2²+16*R3²=32): Bit Label [x, y] Coordinates 00000 [−R3 *{square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 00001 [−R3 * {square root over (ε_(x))} *sin(π/8.0), R3 * {square root over (ε_(x))} * cos(π/8.0)] 00010 [R3 *{square root over (ε_(x))} * sin(π/8.0), R3 * {square root over(ε_(x))} * cos(π/8.0)] 00011 [0, R3 * {square root over (ε_(x))}] 00100[−R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 00110[R2 * {square root over (ε_(x))} * sin(π/4.0), R2 * {square root over(ε_(x))} * sin(π/4.0)] 00111 [R2 * {square root over (ε_(x))} *sin(π/12.0), R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 01000[−R3 * {square root over (ε_(x))} * cos(π/8.0), R3 * {square root over(ε_(x))} * sin(π/8.0)] 01001 [−R3 * {square root over (ε_(x))}, 0] 01010[R3 * {square root over (ε_(x))} * sin(π/4.0), R3 * {square root over(ε_(x))} * sin(π/4.0)] 01011 [R3 * {square root over (ε_(x))} *cos(π/8.0), R3 * {square root over (ε_(x))} * sin(π/8.0)] 01100 [−R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 01101 [−R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 01110 [R2 *{square root over (ε_(x))} * sin(5.0 * π/12.0), R2 * {square root over(ε_(x))} * sin(π/12.0)] 01111 [R1 * {square root over (ε_(x))} *sin(π/4.0), R1 * {square root over (ε_(x))} * sin(π/4.0)] 10000 [−R3 *{square root over (ε_(x))} * sin(π/8.0), −R3 * {square root over(ε_(x))} * cos(π/8.0)] 10001 [0, −R3 * {square root over (ε_(x))}] 10010[R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 10011 [R3 * {square root over (ε_(x))} *sin(π/8.0), −R3 * {square root over (ε_(x))} * cos(π/8.0)] 10100 [−R2 *{square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 10101 [−R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 10110[R2 * {square root over (ε_(x))} * sin(π/4.0), −R2 * {square root over(ε_(x))} * sin(π/4.0)] 10111 [R2 * {square root over (ε_(x))} *sin(π/12.0), −R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0)] 11000[−R3 * {square root over (ε_(x))} * sin(π/4.0), −R3 * {square root over(ε_(x))} * sin(π/4.0)] 11001 [−R3 * {square root over (ε_(x))} *cos(π/8.0), −R3 * {square root over (ε_(x))} * sin(π/8.0)] 11010 [R3 *{square root over (ε_(x))} * cos(π/8.0), −R3 * {square root over(ε_(x))} * sin(π/8.0)] 11011 [R3 * {square root over (ε_(x))}, 0] 11100[−R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 * {squareroot over (ε_(x))} * sin(π/12.0)] 11101 [−R1 * {square root over(ε_(x))} * sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)]11110 [R2 * {square root over (ε_(x))} * sin(5.0 * π/12.0), −R2 *{square root over (ε_(x))} * sin(π/12.0)] 11111 [R1 * {square root over(ε_(x))} * sin(π/4.0), −R1 * {square root over (ε_(x))} * sin(π/4.0)].